Why does ex bring me around family but says he makes sure I know we’re not together?

Anonymous
We dated for 3 years. Broke up 9 months ago. We still see each other every weekend and sometimes even throughout the week. We still go out to dinner, dates, he brings me around family, took me to his daughter’s graduation, I still obviously stay at his place since we don’t live together anymore I cook for him vice versa, I wash his clothes. But he makes sure he lets me know he loves me but we’re not together. He talks and hangs out with other women (new women he’s meeting online). Wth? Should I wait for him walk away give him the silent treatment (but if I do I’m scared he won’t come back because yes I do love him) why this behavior? And also he tell me I can do the same and go have “friends” but when he thinks I met someone or thinks I’m talking to someone he seems irritated and says who are you talking to boyfriend, who is it, mhmm lmc etc why?
Why does ex bring me around family but says he makes sure I know we’re not together?
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