This is going to need some context and a brief overview of history.
The Geography and Economy of Iron Islands
As you know, Iron Islands are, well Islands. To maintain trade, to raid, to conquer and to defend their Isles, like any other Island nation the Ironborn need a strong naval fleet.
The lands of the Iron Islands are extremely poor. They are mostly barren and those that aren't are often plagued with storms that destroy whatever they could hope to sow. The people lack even the basic domestic animals to help them sow crops and the Iron Islanders often have to do the tilling and other stuff themselves. If not for the Fishermen (Estimate by Archmaester Haereg is that 7 out of 10 families in Iron Islands are Fishermen), the Iron Islanders would have starved to death long time ago.
All these differences, Archmaester Haereg asserts in his History of
the Ironborn, are rooted in religion. These cold, wet, windswept
islands were never well forested, and their thin soil did not support
the growth of weirwoods. No giants ever made their homes here, nor did
the children of the forest walk what woods there were. The old gods
worshipped by these elder races were likewise absent. And though the
Andals did reach the islands eventually, their Faith never took root
here either, for another god had come before the Seven: the Drowned
God, creator of the seas and father of the ironborn.
The Iron Islands
Furthermore given the condition and the size of their lands, it is possible that they are perhaps just as small a Population as the Dornish, if not more. Their mines yielded none of the precious and profitable minerals.
Poor in aught else, Iron Islands are rich in Iron, Tin and Lead mines. These ores were used to make weapons for the raiders. What was missing now, was the wood to make ships. Once that was done, The Greenlanders would be kneeling in their septs and Godswoods praying "From fury of the Ironmen, Oh Lords deliver us".
Such riches as the Iron Islands possess lie under the hills of Great
Wyk, Harlaw, and Orkmont, where lead, tin, and iron can be found in
abundance. These ores are the chief export of the islands. There are
many fine metalworkers amongst the ironborn, as might be expected; the
forges of Lordsport produce swords, axes, ringmail, and plate second
to none. The soil of the Iron Islands is thin and stony, more suitable
for the grazing of goats than the raising of crops. The ironborn would
surely suffer famine every winter but for the endless bounty of the
sea and the fisherfolk who reap it.
TWOIAF: The Iron
The Days of the Old way: What happened and why?
In the old days, when Ironborn were just starting sailing, there were great forests in Great Wyk, Harlaw and Orkmont. But since Iron Islanders needed ships to take everything else they needed, those forests took so much damage that in the end those forests were wiped out. It was at that moment that the Ironborn, until then content with raiding, turned to conquest. There were plenty of forests in the Mainland and Ironborn wanted them.
Archmaester Haereg has argued that it was a need for wood that first
set the ironborn on this bloody path. In the dawn of days, there were
extensive forests on Great Wyk, Harlaw, and Orkmont, but the
shipwrights of the isles had such a voracious need for timber that one
by one the woods vanished. So the ironborn had no choice but to turn
to the vast forests of the green lands, the mainland of Westeros.
All that the islands lacked the reavers found in the green lands.
Little and less was taken in trade; much and more was bought in blood,
with the point of a sword or the edge of an axe. And when the reavers
returned to the islands with such plunder, they would say that they
had "paid the iron price" for it; those who stayed behind "paid the
gold price" to acquire these treasures, or went without. And thusly,
Haereg tells us, were the reavers and their deeds exalted above all by
singers, smallfolk, and priests alike.
TWOIAF: The Iron
Their small size, lack of suitable lands to sow crops, lack of any precious minerals and harsh weather are precisely why the traditions of raids developed in the Iron Islands. The Greyjoy words may be "We do not sow" but a more precise phrasing would be "We can not Sow" which was given a heroic makeover to attract the youth of the Iron Isles to take what they needed to survive by raiding others. As the population is presumably very small and the role of raiders is essential for their survival, The Ironborn also capture captives who they then enslave to work their mines while the native population is focused on raiding and sailing. That's why they now hold those professions in contempt, because their thralls used to do that. They seem to have forgotten the days when they themselves did all that until the raiders started bringing slaves.
Now at that moment, the coastal lands of the Western Westeros were thinly populated. And none of the Kingdoms on the coasts had developed shipping technology on par with the Ironborn. At best they could come up with cogs and small boats which were not able to challenge the Ironborn longships on open seas. When Winter would hit, Ironborn would strike to find food for their people. The raiders did so well that they fed the entire islands in the Winters. That's how "We do not sow" became Greyjoy slogan.
The lands the reavers plundered were densely wooded but thinly peopled
in those days. Then as now, the ironborn were loath to go too far from
the salt waters that sustained them, but they ruled the Sunset Sea
from Bear Island and the Frozen Shore down to the Arbor. The feeble
fishing boats and trading cogs of the First Men, which seldom ventured
out of sight of land, were no match for the swift longships of the
ironmen with their great sails and banks of oars. And when battle was
joined upon the shores, mighty kings and famous warriors fell before
the reavers like wheat before a scythe, in such numbers that the men
of the green lands told each other that the ironborn were demons risen
from some watery hell, protected by fell sorceries and possessed of
foul black weapons that drank the very souls of those they slew.
Whenever autumn waned and winter threatened, the longships would come
raiding after food. And so the Iron Islands ate, even in the depths of
winter, whilst oft as not the men who had planted, tended, and
harvested the crops starved. "We do not sow," became the boast of the
Greyjoys, whose rulers began to style themselves Lords Reaper of
TWOIAF: The Iron Islands
Evolution of Customs
Now since they had a supply of slaves who they set to farming and mining, the opinion of those professions took a hit in the Isles. They were jobs fit for thralls and slaves exclusively, not for any Ironborn. Contrary to that, Ship-wrights remained exclusively Ironborn. The raiders were the highest regarded folk in the Isles and could there be any raids without the Ship-wrights building them ships? They were the backbone of the new culture and traditions of the Isles, whose lynchpin was raiding.
The Age of Conquest: Driftwood Kings
With successful raiding, the economy boomed. With the influx of the Salt-wives, the population boomed as well. Now was the time to seek permanent settlements in the Greenlands. And so the Ironborn went to war again and the Firstmen, helpless before their naval might, either abandoned the shorelines or paid tributes to keep their crowns.
But of course, situation doesn't remain the same forever. Eventually the Firstmen learned how to build longships and then the Firstmen resurgence began. Gardeners and Hightowers were the first who stopped paying tributes and others followed their lead. The Lannisters went even further and became the first Mainlanders to raid the Iron Islands themselves. The tables had turned.
Anyhow eventually the Ironborn were thrown back to their Isles by the Targaryens and were forced to bend the knee. They were beaten but their traditions remained intact.
Capturing Military Fleets
In the early days, the Ironborn had the best maritime technology, they did not need to steal poorly constructed vessels of the First Men.
In current timeline, The ships of the Mainlanders are larger and more formidable than the Ironborn vessels but the Ironborn vessels are faster, more durable and have better crews. That however doesn't mean that they could go and capture a whole military fleet without battle. And in a battle, they would be severely outnumbered and outgunned (Out-axed?).
They do steal Essosi trade ships etc on open seas when it is convenient but military ships are a different sort of beast. It is near impossible to capture a fleet without battle and in battle, many of them would be severely damaged.
That doesn't mean they do not capture military vessels that surrender or are overwhelmed. But capturing isolated vessel or remnants of a defeated fleet is different than let's saying dropping in some commando-style units behind enemy lines and have them take over an entire fleet at anchor. They won't likely be left without a crew and the port defense would make it impossible for the infiltrators to get away without the whole fleet sailing into battle position.
That's also why even when Euron sneaked close to Lannister fleet during Greyjoy rebellion, he merely set them on fire as he had no hope of taking them over without a battle and in a battle his chances were grim. So he just took the Lannisters by surprise and temporarily dealt with the threat their fleet posed to the Iron Islands. Of course the Lannisters quickly built another fleet and joined the Royal fleet where they together smashed the Iron fleet and destroyed the rebels.
So in conclusion:
- The boast of "We do not sow" is just that. If the Ironborn had any better alternative, they would not have become brigands. They may boast all they want but without the Tillers, Miners and Fisherfolk, they would all die.
- Building ships is one of the proud traditions of the Iron Islands.It is not considered a menial profession like farming and mining. Their ships are fast and strong. It is unclear if the craftsmanship of other nations compares to theirs. Note that as per the traditions of the Iron Islands, the thralls were forced to work the fields and the mines but the Shipwrights have always remained Ironborn.
- You need a fleet to capture a fleet in the first place when you are an Islander. Ironborn prophets and priests are yet to perform the miracle of splitting the sea, to allow the Ironborn walk to the nearest Mainland port and steal the ships. Until that happens, they need the ships.
- Ironborn do capture odd, isolated merchant and military ships after naval battles and chase. They have never captured entire fleets using land-based parties however.