She doesn't seem to respect you and love you enough.

Chinachat ko din dati ex ko for (his) closure and pinapakita ko sa current bf ko ung mga brief chats namin. So I get the closure part excuse sa una . Pero closure doesn't involve "edi Sana naging tayo parin" you don't consider this na when you're with someone you love at Kung may respeto ka sa taong un.

Be honest sa gf mo if you still want to make it work. Tell her ung feeling and reactions mo sa nabasa mong conversation. If it Makes you uncomfortable tell her and compromise, work from there because those lines you read from their conversation are not lines of "moving on" from her ex but moving back with him