I can be insensitive sometimes, how can I work on not being insensitive?

Just put yourself in her position imagine the" boot on the other foot" how wold you like it, if someone said that to you.. or did that to you.. e.t.c.

Stay up late until the point which you feel all you want to do is sleep (at around 4:32am); proceed to watch a film such as 500 days of summer or the notebook at this point out of tiredness you will feel sensitive whilst watching the film. As these films are about hollywood relationships they will make you feel good will overcome evil and carpe diem should be your motto in life and relationships... Repeat if effects wear off. They may be riddled with crap such as good always overcomes evil but they do show that sensitivity is something we all should have!

Secondly - your ex girlfriend said you were insensitive; perhaps there's a reason why she is an ex and she may be saying that because she is your ex!