Deleted items don't go into trash
There are two likely possibilities:

First, you're accidentally holding down the Option key or it is stuck - do you get the same behavior if you use a different keyboard?

Second, the permissions on your ~/.Trash may have become corrupt; run Disk Utility from your /Applications/Utilities folder and verify permissions on the drive containing your home folder - if errors are reported, restart from Recovery Mode and run Disk Utility again.