Sam's father wanted to get rid of him so his younger brother could become the heir; he threatened Sam and forced him to join the Night's Watch. Ok, fine, but I have some problems with this. First: why the Watch? Given that Sam was a bookworm, if would've made much more sense to send him to the Citadel; this would also achieve the same purpose since Maesters forgo any claims and titles. Second, given that Sam had "chosen" to take the black out of free will (i.e., he wasn't a criminal), couldn't he just say he changed his mind after arriving on the Wall and so leave (before taking his vows, of course)?
You may have missed that Sam had already explored the option of becoming a maester with his father. The result was that Lord Tarly said something to the effect of:
If you want to wear a chain, so be it.
...And chained him in the dungeon. Lord Tarly is a hard man, and has been trying many different things to make his son into what he wanted him to be. Allowing him to become maester would not be something he wanted.
As Sam says in AFFC/ADWD, the life of a maester is servitude, and no son of Lord Randyll Tarly could humiliate himself in that way. In the Night's Watch, Lord Tarly figures that Sam might finally become the hardened man he always wanted him to be. Although I don't think he really cares, he just wanted him gone, so his younger son Dickon could be his heir.
Finally, of course, Sam cannot exactly leave the watch. As long as he is alive and a free agent, he threatens Dickon's inheritance, so Lord Tarly would probably have him killed.
Sam's father wanted Sam to disappear, and if that meant death, so be it.
In fact, I believe that was exactly the choice his father gave to Sam: take the black, or risk dying in a hunting "accident".
The life of a Maester is a relatively soft, easy life, and Maesters live to a very long age. Life on the Wall, on the other hand, is hard and dangerous, and many don't survive the first few years.
Sam's father was hoping Sam would die quickly, without leaving any blood (figurative or otherwise) on his own hands. Killing your kin is one of the biggest taboos in Westeros, but it doesn't prevent people from wishing their own kin dead, or even trying to bring it about indirectly.
Sam's father hated him and the man he might become. His father has a reputation as a seasoned warrior with successful battles to his credit. Seeing Sam lay about reading with his mother and living a life he thought was not masculine in its tone is something Tarly could bear.
Sam's option was leave or be killed in a hunting accident.
I'm not at all sure this is backed up by the books, but perhaps House Tarly, being Targaryen loyalists (well, they used to be anyway), are anti-Citadel.
After all, the Maesters spent centuries plotting and putting in motion the demise of the Dragons and of House Targaryen. And perhaps House Tarly is aware of this fact, or even just vaguely aware of it. If that's the case, Randyl would not want the Citadel to have what is somewhat of a hostage or double agent.
So - better Death than Maestership for any Tarly!
(This might also have something to do with House Hightower, but that's too speculative and out there so never mind.)