Define Dating

So the guy I've been seeing this guy for a while now. For some reason, he asks me if its okay if he's with me but is also allowed to see other women because we're "just dating" and not exclusively together together. For obvious reasons, this revelation has put me on edge but i don't want to lash out before making sure i have every right to be offended or I'm just overreacting

So help me out please. What is your definition of dating?

Because to my understanding, if we're dating, we are 'together together'. Its not an engagement or a marriage but i thought dating meant seeing each other and no one else. If he wanted to see other people than why fuxk with my feelings. I don't want him seeing other people coz we are dating. But apparently my definition and his definition didn't match up.

Help a girl out. I don't know how to appropriately react at the moment.