first, you are mixing up the concept of "limit" with the concept of "infinity"
second, you are arbitrarily assuming that space is "linear" (i.e. you are assuming that if you keep moving in the same direction you will never reach the spot you started from)
third, you are assuming that space is not expanding faster than anything could possibly move
Of course, I am not considering the pragmatic view of the universe. The thought experiment was to show that a theoretical, a priori view of a limited universe is absurd. Whether, this means that the universe is linear, non-linear or expanding is an open question that comes after the initial theoretical point.
As it is, the current cosmological model of the universe does posit a linear, infinite universe.