Are you using a spool? Could it be catching on the little notch that you secure the end into? This has happend to me MANY times before...Now I usually check as I am threading from those spools.
Also sounds like something is too tight..snapping to me means its getting caught on something, or tensions need to be backed off a bit-even if your stitches look good to the eye. Deep breaths! Panicking does not help matters as your machine can 'sense' that!