Can someone please explain how in Star Trek: Discovery they say they haven't seen a Klingon in 100 years but the main character's family was killed by Klingon and she couldn't be much older then 30 years old.
This seems like a clear contradiction.
Is there evidence that Burnham "saw" a Klingon in person, or that the attack on her home was simply an orbital bombardment? We don't know exactly what happened at Doctari Alpha.
The admiral says that they have been in a 'cold war' with the Klingons and that they have had 'fleeting run-ins' with them over the century. Not zero interactions.
Also - remember that Burnham is not just any human.
She was raised on Vulcan
which apparently has had more interaction and possibly more diplomatic ties w/ the Klingons than the Federation
I may point out that in TOS "Balance of Terror" nobody has seen a Romulan in 100 years and yet a Romulan war ship destroys outposts along the Neutral Zone, killing the crews of those outposts.
Actually by the time of "Balance of Terror" nobody on the Earth and Federation side has ever seen a Romulan, realized that the Romulan was a Romulan, and lived to report to other people that was what Romulans look like. Ever. Even during the bloody Romulan war a century earlier when many Earth and Romulan ships were destroyed and their crews killed, there was no report about what Romulans looked like.
So if someone said literally that nobody has seen a Klingon for 100 years, that is still consistent with Klingons sometimes killing Federation citizens like Michael's family and vice versa.
And if someone actually said there has been little contact with the Klingons for 100 years that means there has been a few contacts and/or conflicts with the Klingons in that period. And thus it would be Michael's bad luck that her family were killed in one of those very rare and unusual contacts.
They specifically reference at least one indecisive battle that was also mentioned by Spock in TOS, and given the timing would have occurred about 10 years before "Discovery".
Human example of today: there's essentially no contact between the outside world and the people of Sentinel Island, and hasn't been since the modern world became aware of them in the 1800s. Yet there's still been brief episodes of conflict between the Sentinelese and people who, intentionally or not, land on the island or get close to it. So they've been in isolation, but that doesn't mean there's no contact.
This claim seems really sketchy, based on the rest of what we're seeing.
Note how broad the claim is, in context of the scene:
BURNHAM: There are Klingons out there. We need to go to red alert.
GEORGIOU: Michael. Almost no one has seen a Klingon in a hundred years.
Georgiou isn't merely saying "Klingons are awfully private and/or stealthy, so we never see them face-to-face." She's saying "There can't be Klingons here, we don't expect to find them anywhere, because nobody encounters them ever." She's skeptical at the idea that encountering Klingons -- hidden, stealthy, secret Klingons! -- is even possible. That doesn't seem to match up to points like the ones I've mentioned.
It's possible the series will go back and resolve this, but so far, I'm inclined to write it off as hand-wave-y worldbuilding, and dismiss it as a one-off error.