Because meg is part of "tar av" You take the socks off of yourself. The sentence does not specify who's socks you're taking off, it specifies who you're talking the socks off of.
If you were to say "Jeg tar av meg sokkene hans", that would be "I take his socks (off of me)"
In Norwegian, it is often assumed that we're talking about our own something(s) when nothing else is specified, rendering the possessive unnecessary in many cases where it would required, or at least natural, in English.
Your translation is definitely a possible one, but not the most likely one for this sentence.