You cannot give it to a friend/brother once you are done playing it, as your other games are also on that account.
Support the developer instead and just buy your brother/friend another one?? And are you really ever going to be finished with Skyrim?? I certainly won't be. Or are you perhaps annoyed that you can't just buy one copy and then install it on your computer and your brothers computer so you can both play it at the same time?? Which isn't allowed anyway.
You agree not to:
...
(d) Except as otherwise specifically provided by the Software or this Agreement, use or install the Software (or permit others to do same) on a network, for on-line use, or on more than one computer, computer terminal, or workstation at the same time;
Nor can you sell it without selling your entire account. They also have the power to take away anything you purchase through them and they don't even have to tell you why.
The same argument can be used against non Steam games. This is from the Fallout 3 retail version EULA.
TERMINATION:
This Agreement and the licenses granted under this Agreement are effective until terminated. They shall terminate automatically without notice if you fail to comply with any provision of this Agreement. Upon termination you shall immediately cease using the Software, and destroy the Software, the Documentation, and the other parts of the Software, and all copies of any parts thereof.
So if they wanted to they could terminate the Agreement and licenses and you can't do anything about it because you accepted the EULA. Bethesda are just as likely to terminate your contract as Steam is, which is to say, they aren't.
Likewise you can't sell it either.
You agree not to:
...
( B ) Distribute, lease, license, sell, rent or otherwise transfer or assign this Software, or any copies of this Software, without the express prior written consent of LICENSOR;
Steam just enforces what's already in the EULA. Deal with it.