Well I have a few reasons for loving them (2nd favorite genre). First, they are extremely simple to start up. Most platformers play by moving the character, jumping (or some form of a more aggressive movement than simply walking/running), and then a certain kind of special move/power-up. Even the adventure platformers tend to have this base setup despite moving into more of the adventure genre with platforming being the secondary.
That is what builds upon the second reason I love them being that in its simplicity to grasp it allows a certain level mastery. When it comes to games where the mastery is in the grasping of the game, it creates more of a polarized player capability levels. Either you are good at or you aren't. Take the fighting genre for example. When it comes to the more technical ones in the genre, there isn't much middleground in your abilities in the game. You have the casual players of the genre and you have the hobbyist of the genre. When it comes to platformers (and many others such as shooters and racers) you have where most people can pick up and play it and enjoy it but then you also have a certain level of mastery. And this is what really is a lovable thing about platformers. We can all make it to the end of the first level of Super Mario Bros., but the greats can do it in a certain time, with certain powerups, with a certain high score, etc. This kind of depth and competition brings about the numerious speed runs and epic competitions for the highest scores which are a drive you get out of platformers that you can't get out of a lot of other genres (or you can get a few out of certain genres but not many have all of them combined).
The final reason I would say I have a love for platformers is they usually keep a simple storyline. Most of them don't harken too much on elaborate stories with characters with a lot of depth. Now whether it is shallow on purpose is another story, but in having that it allows for expansive settings, vast amount of unique characters, and artistic creativity. This is pretty obvious in the amount of "worlds" you see in platforming games along with most of them having lots of unique enemies, bosses, and allies. Also why platformers usually have some of the most diverse artistic designs, sometimes varying within the game itself. So not only do you have varying worlds and characters, but varying atmospheres to fit each. This is my main draw to platformers as it really does seem to be unique. In ironic fashion, it is the simplicity of the game that allows for such expansive and complex variables.
So I can understand that platformers aren't for everyone. And you seem to like action-adventure games which is my number one favorite genre. Just platformers are very hit or miss which can obviously leave a bad taste in your mouth. Either you've created a good platformer or a bad one. Personally, I've found very few platformers that fit the good, while many tend to hit that miss simply because they aren't easy games to craft well. They are easy to make, but not easy to master. It's easier to make a good run of the mill shooter or racer or fighter or even adventure game. But not platformer. The elements requiring it to be good aren't based on a central main character or plot. Instead it is based acute level design, precise mechanics, and a vast imagination. And those are hard to come by.
So if you want any suggestions, look no further than Super Mario Galaxy or any Mario game. It really is perfection in platforming. Despite my love for Banjo-Kazooie, Lego games, Sonic games, etc., there really is nothing better than playing a Mario platformer. It's the top one in the genre for a reason. But if you don't like Mario, then it only goes down from there so that would be a way of figuring out that you don't like platformers. Hope htis helps.