I go "into" a supermarket, which is just a glorified market; in everyday usage I would say "I'm going to Sainsbury's later", but if I were talking to someone on my phone about to enter the shop, I'd say "I'm just going into Sainsbury's now". Similarly when I buy my vegetables at my local covered market, I walk "into" the covered market. I agree that "toward" is a valid translation, but that wasn't on the list - but "to" and "into" both were. I think either "into" should be accepted, or it simply shouldn't be there as an option.
What you say may be true, but "into" would be translated differently in Latin.
In forum eo. -> I go into the market.
Ad forum eo. -> I go to/toward the market.
Ad + accusative doesn't imply that the person reached their destination, just that they are going toward a place. In + accusative provides the meaning of entry / successful arrival.