There is a thread about this subject on the “Ask Andy About Clothes” Website forumhttp://www.askandyaboutclothes.com/forum/showthread.php?78791-Tie-stripes
Aside from a lot of rubbish about the English slope leading the eye to the head while the American leads the eye down to the crotch, the reason given is that the English were very protective of their Regimental / School / Club tie patterns so the Americans reversed the stripes so not offend anyone or be accused of wearing something to which you are not entitled.
This is confirmed on the “A Suitable Wardrobe” Website. Will Boehlke wrote much the same in a Blogg a few years back.
“Since men began wearing neckties, the direction of the stripes on striped versions have traditionally gone from higher on the left to lower on the right, just as a man's coat buttons left over right. The direction is aesthetically pleasing, and complements a man's pocket square and boutonniere on the left side of the jacket.”
“Right hand high necktie stripings originated when Brooks Brothers brought the regimental tie to the States during the 1920's. BroBroClo deliberately reversed the direction of its stripes as a way of placating the English, some of whom might have been tiffed to find an American businessman wearing an old Eton necktie or suchlike without actually attending the school. Other American tie makers like the Robert Talbott Company did the same ... and the practice has continued in that country, whether the ties are regimental or not.”http://asuitablewardrobe.dynend.com/2007/03/how-to-stripe-necktie.html