What does it mean if a guy gives you his number to "text him sometime"? I feel like he might have felt sorry for me:/

(he did it after I told him about some problems in my life?) 

As far as i can get the memo, what he's done is a hint/sign of his interest in communicating with you.

Whether he felt sorry or not it's part of a untold story, a story that you never mentioned. So we can't tell if he did or not because we don't know why would he.

What do you think it means when someone wants you to text them or vice versa? If they hated you, they wouldn't waste their time. In addition, why would they want you to clog up their phone with your texts if they didn't want to receive them?

I don't know of any guy who would give his number out of pity. If he wasn't interested he wouldn't have given you his number.  It sounds more like you are having some self esteem issues. You need to start feeling a bit more sure of yourself. You have his interest and his number now text him!

Sounds like you found a potentially nice person. Text him and see how things slowly develop.

I think it means he wants you to make him some soup...