You are likely doing nothing wrong. They keep making that cooler worse and worse. I installed one a couple years ago with no issue but built one for a friend a couple months ago and struggled to get them to thread too. I did finally get a helper to hold the board so I could use both hands to get the screw in.
In reality I replaced mine as it was frankly a horrible cooler anyway. I got a 212 evo for 35 bucks and it tricky compared to some to mount but nothing like that stock cooler has gotten and boy does it cool much better.
Like I said I just had a friend hold the board with one hand and push against the back plate and use one of my hands to grip the cooler and the really bared down on the screw driver to get it to go. It should not be that hard.
If you want to verify you don't have anything setup wrong you could take a pic of both sides of the board and post it here and we can be sure.