What kinds of issues to people have with the police exhuming their loved ones bodies?

I’m in the midst of a Law and Order: SVU marathon and in this particular episode, the police want to exhume a body to get DNA. I watch/have watched a fair number of police and forensic shows and I see this issue often. The family members of the deceased always seem insulted and disgusted that the police are asking to exhume the body.

I’m just curious as to why. I understand that there are respect issues and even the issue that loved ones may have trouble moving on from a death but if the police want to exhume a body to help solve a murder, why would there be so much issue?

In truth, I have no idea what I would want to do in this situation simply because I’ve never been in the situation but I feel as if my mother would want me to let the police exhume her body if it could help solve a murder.