Disadvantages of Group Travel
No privacy. If you're someone who values their privacy, group travel may not be for you. There could be very little chance to have any time to yourself when you're within a group, especially if you're sharing a hotel room or staying in a hostel.
Clashing personalities. If you don't get along with someone in the group, traveling with them isn't going to suddenly turn you into best friends. It can end up being awkward and uncomfortable for everyone involved. On the other hand, if you generally get along with someone, you might discover that traveling with them can put strain on your relationship, particularly if you're not used to spending long stretches of time with them.
Different interests. Not everyone is interested in the same thing, and it's not always fun having to go along with a group when you're not interested in what they're doing. Your friends want to hit the beach but you'd rather check out a museum? You want to go on a bus tour but your friends would rather take a walking tour? Little things like that might not seem like a big deal, but if you constantly have to compromise to keep the group happy, your fun vacation can turn frustrating very quickly.
Advantages of Solo Travel
You're the boss. You get to call the shots. There's no one to tell you where to go or what to do, and you don't have to make compromises. You can do things at your own pace, on your own timetable.
Meeting new people. For some people, meeting other travelers is part of the draw of traveling alone. A lot of solo travelers seem to end up in the same spots, so you have a chance to meet other people with the same interests. You can join them for some companionship so you don't become a complete hermit, then go your separate ways.
Reflection. Some people take trips alone because they want time on their own to reflect. If you simply enjoy your own company, or want to be with your own thoughts without anyone else intruding, solo travel might be the way to go.