I asked a family member to co-sign for me to get a loan from the bank, at first they said they might do it for me, but the second time I asked, they told me that they don't let people co-sign any more. Is this true or was this person just avoiding signing for me?

I have never heard of anyone not allowing you to have a cosigner. I have had a cosigner and had no issues with it. It could be because it's a bank loan but I am not real sure about that.

Sounds like they don't want to do it, only the lender you want to use will know if they will allow it or not, every lender I know still does.

But again I don't blame them, since if you don't pay, they will have to.
And that is why the lender wants a co-signer.

I do blame them, because it's my parent and they know I need the money for a medical procedure and they also know I have the income and nearly a thousand dollars of emergency money saved up to pay the loan off.

I live in Canada but a few years ago I tried to "co-sign" for my son for an auto accident payout and our bank did say, they do not do co-sign loans. It was about a $3000 amount. I'm not sure why, but maybe for larger amounts.. I ended up getting a line of credit (in my name).