Most free jazz players are guys who have been listening to and playing music non-stop for decades. So even as they're rejecting some or all of the basic tenets of straitlaced music as we know it, they're still doing musical things. Sometimes they're reacting against one or more aspects of music in a pointed form of experimentation - like stuffing chords inside each other, or playing solos against each other in different keys or with competing internal rhythms. Sometimes they're playing strictly with the less-appreciated musical ingredients - timbre, or rhythm in the most basic sense: sounds and the spaces between them, but without meter or pulse - and by divorcing these aspects from the constraints of melody and harmony and conventional rhythms, they can do something more striking and unique with them.

Most free jazz, and especially all free jazz by the greats mentioned in this thread, is still musical even as it comes off superficially as aggressively unmusical. That's what is cool about it, and as you give it repeated chances - especially if you come at it from a background steeped in music and jazz in particular - you might find something likable about some of it. I did eventually. Still not much of a fan of "Ascension" though.