She broke up with me but why do this?

So this woman broke up with me and said she needed space. I tried to fight for her once and then stopped. Immediately went into NC. For the next week, she would always text me and I would reply but kept my distance. One day, she said "guess you were in it for the sex". I replied with I thought you wanted space.

Following week, she was extremely friendly and always trying to talk to me. She ended up getting frustrated and I find out that she started hanging out with an acquaintance of mine who never knew about us. At first, what was happening seemed a little iffy. I simply brushed it off and kept to myself. Nothing ended up happening which was good.

For about 2 weeks, she seemed very upset. She couldn't be in the same room as me. Her kids would want to say hi to me and she would say "no". Her back would always face me and she just genuinely seemed upset with me.

After those 2 weeks have passed, she started being friendly again. Was teasing me, play fighting me, and just being extremely friendly. Again, I kept my distance.

Last Thursday, she greet me asking how I was. I responded without reciprocating an answer. After, I walked right by and she cracked saying "you can't just keep ignoring me". I pretended as if I didn't hear and asked what she said. She didn't repeat and seemed frustrated.

The last time I saw her was Tuesday and she seemed a little sad. She was looking at me a lot according to my friends. I acted as if it didn't bother me. Then, when I was talking to one of my friends, she was 3 feet away staring at me.

Why is she doing this?
She broke up with me but why do this?
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