Interesting! It might be your therapist felt it that whole time, or perhaps means something different to what I mean.
For me it feels like a form of nervousness mixed with excitement and attraction. It's not an unpleasant nervousness, not dissimilar to the feeling of jumping into a cold pool, exciting, refreshing and a bit of a shock to the system. With a new person, there is extra-vulnerability to opening up to them for the first time, so I think the spikey nervousness just makes me extra alert to the other feelings.
As a relationship continues, the butterflies slowly go when I feel more safe and trusting, I could still frequently excited to be around them and enthusiastic about the relationship but in a calmer way. It has also gone away when I have discovered things about them that I don't like, and the enthusiasm portion has dropped out.
On the flip-side, I have also felt a comparable feeling in relationships that were unhealthy or abusive and needed to be over, where the connection wasn't actually that authentic. The instability of the relationship can provide that nervousness again, and it can help make the moments which do feel a sad nicer also a tiny bit more thrilling. It is really not helpful in getting out, or ending a doomed union, but it can mean there is at least the consolation prize of an available nice feeling leading up to the ending that has to happen.
In situations like that it's been really important that I ignore 'the butterfly feeling' and treat it as unreliable information, this has really helped me make the steps needed to move on.
"In between two tall mountains there's a place they call lonesome.
Don't see why they call it lonesome.
I'm never lonesome when I go there." Connie Converse - Talkin' Like You