Arms and hands were not always held rigid during solo dances. Previously they were sometimes more relaxed and were even placed on hips. It seems that the influence of parish priests led to the lack of arm movement; some argue that stiff arms were less provocative, others argue that the Church was trying to increase dancers' self control. Hand movements still occur in figure (group) dances.
Speculations on Why Arms Aren't Used
1. I heard that English soldiers would tie people's arms down with rope and make them dance, though I hardly think that that would be a treasured tradition to continue!
2. I've also heard that the Catholic church made the use of arms prohibited, because using your arms was seen as flirting.
3. The reason I heard that dancers keep their hands by their sides is this: When the English invaded Ireland, they didn't allow the Irish to do anything fun, including dance. Some of the Irish people had been turned out of their homes and were put in large rooms for a while. These had glass panels starting at 1-2m off the ground so the English could see what they were doing. The story is that the English could only see the top half of the Irish, so when they danced to cheer themselves up, the English saw stern faces and straight arms and thought people were exercising around the room when really, their legs were wildly dancing!
4. They also used to dance sitting in their chairs which forced them to keep their upper body stiff while their feet went a mile a minute! They did this for the same reason -- fear of the English looking in the window!
5. One theory that I heard was that the dancing was too provocative, so priests made them keep their arms down...it increased their self control.
6. Another one is that they were prisoners so their arms were chained to their bodies, leaving it up to their feet.
7. I heard that the French dance masters came to Ireland and tried to teach them to be more controlled and dance less wildly.
8. Yet another story is that when the English invaded, they made the Irish come dance for them to entertain them. So the Irish kept their hands stiffly at their sides to out of disrespect for the English infidels. I've also heard that Irish pubs are so crowded that there's no room for moving your arms when you dance!
9. It's just like the Irish to make a dramatic story out of everything, but the most sensible reason for the hands-at-sides tradition is that since the focus of Irish dance is on the elaborate footwork, the use of the arms and hands simply detracts. As a matter of fact (so I've read) the complete absence of arms and hands is a fairly new development (like the "authentic gaelic dress" we see at feiseanna!) and even at the turn of the century some use of arms and hands was typical.
10. I've Heard that when England invaded Ireland they forbade them to dance. So when the Queen/King looked out the window to the Irish people they saw them jumping up and down. They made it look like that wanted to see the Queen/King