Nobody would pack a rifle doing this around the corrals, but if I was working alone out at the far end of the forestry lease, you can see how a forward facing rifle on this side would be in the way of the rope. I rope right handed and after I rope her I'll go to the horn and take a couple of wraps. Depending on the cow, I can let rope run, pop it off the horn and re-wrap, take up slack and re-wrap, etc over and over basically playing the heavy animal like a big fish. Better for the cow so I don't choke her down, better for my horse so he doesn't get jerked by a big animal hitting the end of the line hard. After I get everything slowed down, I can put a trip on her and get her down. Keeping the rope tight between the horse and cow, I can tie off on the horn and step down. My horse will hold the rope tight, and I can tie the legs of the cow with a little short rope in my belt. Then I can needle her, or whatever.
A rifle might get hung up and that would be bad. Even a rifle with butt to the rear on this side could be a problem as lots of times I'll face my horse away from the cow until she calms down after I've roped her. With heavy cattle, 1500 lbs or so, facing away takes the pressure of the rope on the horn off my horse's shoulders and distributes it along the saddle and out the back end. Little tricks of the trade.
Sooooo....I'll try packing the rifle on the near side and just get off once in awhile and reset my saddle. Hope this answers your question.
FIXED!