Should I break up with him?

I started dating someone for about 3 months now. He has already told me he loves me. However, recently I questioned him about his previous relationship and ex-girlfriend. He said he still communicates with her and part of him will always love her (his ex). This was really upsetting and I haven’t spoken to him for 2 days. Should I break up with him?I don’t believe someone should still love their ex.