Well, there's a really simple answer for this: age. JFK was born 8 years before Robert and 15 years before Ted. Initially Joe Kennedy Jr. was the great political hope of Joe Kennedy Sr, who had hoped he would become the first Catholic president of the US. However, Joe Jr. died in 1944 during the war (in an accident involving a fascinating top secret plan to fly remote controlled B-17s chock full of explosives into high value targets). After his death the mantel for those ambitions fell on the next oldest son of the family, John.

JFK himself became a war hero, as his tiny torpedo boat (PT-109) was cut in half by a collision with a Japanese destroyer and subsequently exploded. JFK polled the surviving crew on whether they wanted to surrender to the Japanese or continue to fight, and they decided not to surrender, instead they swam for four hours (JFK hauling a severely wounded crewman the whole way using a life jacket strap clenched between his teeth) to a nearby island (and then later swam to other islands) before being rescued several days later. The event received a fair amount of attention in the press as Joe Kennedy Sr. was already famous at that point.

On his status as a war hero, his Kennedy heritage, and, of course, his charisma and other qualities (and Joe's massive bank roll and influence) JFK won election in 1946 to become a congressional representative for Massachusetts. At that point Ted Kennedy was only 14 and Robert 21 (and still attending Harvard), neither legally old enough to run for congress. Six years later JFK won a Senate seat, and even if Joe Kennedy Sr. had decided Ted or Robert were better bets, neither had any sort of political resume at that time due to their age.

And, indeed, both Ted and Robert could be fairly have said to have ridden JFK's political coat tails. Ted took over JFK's senate seat after it was vacated, and RFK was appointed attorney general by Kennedy when he became president.