Why would my ex still text me everyday, if he's the one who broke up with me?

Anonymous
Long story short, I found out he's been talking (and god knows what else) to some other girl. Of course he denied that there's something going on between them and they're just friends. In the middle of the argument, since I wasn't believing him, he said that if I want to break up, then we break up. Yet, since that day he still texts me everyday to say good morning or ask how's my day been and keeps the conversation going. Should I ask him what's going on in his mind?
Why would my ex still text me everyday, if he's the one who broke up with me?
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