Take a length of thread off the spool and wind it around your fingers as if you were going to be using it like dental floss. Put your thumbs against it in the middle and stretch it. If it breaks easy, it's your thread that's the problem and you need to toss that thread. Even though the thread is new, it could be a bad batch.
You also might have a burr on your throat plate. Check it to be sure because that will definitely fray/break threads.