Of the six sports you mention, the International Olympic Committee recognizes five as Olympic sports. [cheerleading is not]
Of the same six, the NCAA recognizes three [not cheerleading, martial arts, or archery] while the AAU recognizes all of those but archery. Many schools do indeed have archery as a sport - the governing body is either NASP (National Archery in Schools Program) or JOAD (Junior Olympic Archery Development) of USA Archery each with interscholastic competition all the way to a national championship.
ESPN (the most comprehensive network of sport news and coverage) covers all of those six as sports though some more regularly than others. Then again, they cover poker too.
What I notice about your list compared to that of your friend's list is that theirs are known as "team sports" whereas all three of yours are known to be "individual sports". Some other individual sports are track, cross-country, gymnastics, swimming, tennis, golf, etc... That's fine, some people prefer sports that rely entirely on their own skill and not so much on the group effort. Others prefer sports that bring a group together as a team.
Your list is also completely "martial" -- that is, your sports are all fighting sports. The foundational nature of archery and fencing isn't scoring points - it's killing things. That's ok though, it just makes your interests different than theirs.
It might be beneficial for you to be involved in some sport that is team based, but that doesn't make yours less valid. You don't need a basketball or soccer team to do your sport - you just need you and an oponent. Then, at the very foundation of what is a sport, it could be said yours is more sport than theirs -- yours depends entirely upon your own skill and ability whereas theirs relies on the cummulative skills of a group of people.
That all said, who cares? As long as you're enjoying it and that they enjoy theirs, it simply doesn't matter much at all.
Archery and fencing are definitely sports. They can be just as physically demanding as ball sports, although they suit more individual athletes rather than those who are team-oriented. There is a mentality from those who do team sports where they tend not to "recognize" other sports as being "sporty" because they aren't in a team, however, archery, fencing and martial arts are considered sports by every sporting organization out there. Ignore them. Archery rules.
Archery can be a sport, although most schools do not offer it. Also, all of these things you mentioned could also be seen as hobbies. As to what your friends say, sports don't really get people anywhere in life, keep focused on your studies and don't waste time with these sports that the school recognizes, they are really a waste of time.
All three are called sports by the IOC and are part of the Olympics, that makes them sports in my book.
