You can go any direction with a longarm, but the stitch is best formed when the machine is moving from left to right (from the front of the machine). It has to do with how the thread comes off the bobbin. I heard a technical explanation once but can't remember the specifics. If you're quilting fairly slowly or changing directions frequently you may not see the difference, but as your speed increases you're more likely to have skipped stitches, shredding, or poor stitch quality (especially on the back) when going across the quilt from right to left. You may also see more needle flexing, which causes skipped stitches.
Here's another discussion on the topic on this board -
Is a Long Arm quilting machine meant to be used left to right?