The things can be looked at differently, and I'll try to explain it.
I'll begin with another verb, брать у ('take from'). The idea of how the preposition
y denotes possession is following:
y actually means "near, at", so
у стены means 'at the wall, near the wall'.
у Петра actually means 'at Peter's'
У Петра есть машина is 'At Peters there's a-car'.
Я брал книги у Петра is something like 'I took books at Peter's.'
And if we speak about отобрать у, it's almost the same, with an interesting exception of the prefix ото- which is a positional variant of the prefix от- derived from the preposition от, 'from'.
What I mean is, this prefix ото- corresponds to the English 'away' in take away from. Since 'away' has almost the same meaning as 'from', it's the English manner of constructing the phrase take away from which looks rather strange, it's almost the same as saying *take from from, while the Russian отобрать у is pretty logical, it's like *from-take at.