I can see the perspective and understand it totally.
I'm not saying it is any worse than the stigma attached to breastfeeding, or possibly even comes close, as I've not experienced that either.
But there are a number of pressure that are placed on women these days around parenting and pregnancy - so many people appear to have expectations, and there is a lot of intense scrutiny about certain aspects by media and others.
I mean, some mums have felt stigmatised by having to have a cesarian FGS! From some NCT groups refusing to discuss the notion, to being labelled by others as 'too posh to push'.
While you may feel that bottle feeding is moer socially accepted - i felt under enormous pressure both before and after birth by the way in which the medical professionals approached the subject of breast-feeding, and the issues I had post birth due to my sons severe tongue tie which they refused to address. I felt incredibly unsupported and judged when trying to seek support in resolving the feeding issues. As a result I had a lot of guilt around it, about not being able to do something that was 'so natural' etc. Especially as so many moms at baby groups etc were breastfeeding.
I'm not saying it compares to your experience at all. But it's still an experience of stress, guilt, non-comfority, feelings of failure.