Can u break up with someone still love them and move on quickly?

My b ex-boyfriend said he wanted to break up last night, He says he still loves me and forever will. I know he does, but he says the realtionship started to get boring. That's because he saw how much him and another girl had in common. He knew he had a girl but continued to talk to her and i guess ended up liking her.Can u break up with someone still love them and move on quickly?
My ex did the same thing. Another girl was on the side and saw how much more in common they were so he started to take interest in her. He told me that he loved me but felt we weren't right for each other in that way so we broke up. Sometimes I feel it's not possible because if you truly love someone, another person no matter how great they are, shouldn't sway you. Sometimes people use the word love instead of saying care. A lot of people don't really love the person but they do care for them. If you love me, that means your heart is all mines an no one can get it. If you care for me, that means you want to see me safe and happy but other people can get in. I felt that if he loved me he shouldn't have been able to date a new girl so quickly after our break up. So I think he cared for me but wasn't in love with me.