I often feel the same way, telling myself I'm a wimp and other things.
It is the depression talking!
The flip side of being a sensitive person is that it gives you the capacity for empathy and the potential to encourage and help other people on their way.
It would be a brutal world if everyone was hard and thick skinned.
When I worked in healthcare, in my induction they told us about the staff support service. They explained that they want sensitive people to work in healthcare because they deliver better care, but sensitive people are more likely to feel pain and stress, which is why they provide the support.
They see sensitivity as a necessary quality, not a defect!