I think we all ask the question in the title at some time or other.
The first painter to pose the question on more than a passing whim was probably Wassily Kandinksy (1866-1944), who has therefore a lot to answer for! 100 years ago he had got the hang of it and was producing spectacular - and puzzling - paintings, a journal (Der blaue Reiter) and essays on art. Far from being slapdash and totally spontaneous (lots of the paintings could fit those descriptions, if one is quite truthful), he thought long and deeply about what he was going to paint. His circle included Auguste Macke (1887 -1914), and Paul Klee (1849-1940), who painted simply hundreds of paintings and, for me, charts the development of abstraction most lucidly because he tried everything that was going at the time and experimented as well. The painters 100 years or so ago really had more scope for innovation than today's, since abstraction was new. Sigmund Freud had a hand in the development of abstract painting, since he was extremely and publicly involved with the subconscious, which plays a big role in non-figurative painting, i.e. once still life, landscape, portraiture etc. have been abandoned.
In other words, the abstract painter paints more or less out of his head! Is he therefore off his head? Of course not, though there are exceptions to every rule. Contemporary "classical" music reflects much of what goes on in the visual arts. Some of it is simply dreadful. Some of it is fascinating. I think we have to remember that when something first appears, it is usually viewed with suspicion. Electricity was probably the most farsighted invention in the 19th century. Radio changed the world - made global communication possible. But there are still people who can't deal with the idea of TV (not the junk, but the invaluable view of the world), and many older people view the computer with suspicion (Help, I think I've deleted the internet). Apparently every third person in the world now possesses a mobile phone. My father died in 1961 dreaming of having colour TV and prophesying that one day we would see people we were phoning. He would have loved today's technology, which is a good reason to go for it myself!
There are lots more inventions one should consider that have changed our world even since abstraction appeared on the scene, some for better, some for worse. A lot of it reflects the abstraction of life itself - and of death, which becomes less and less abstract the older one gets. Much of what is "new" is repetitive.
Since World War II we have seen another explosion of abstract painting, aided and abetted by the development and refinement of acrylic paints, which dry quickly and are thus easier to handle for spontaneous "outpourings" or layered and highly textured work.
In fact, abstract painting often seems to be dominated by the exploration of the materials themselves. I have instruction books devoted entirely to scratching and patching methods (my description!). It is apparently possible to be successful without actually being able to draw or paint these days, especially if you have good marketing strategies, a conscientious agent and a huge ego. If you are in a position to command them, a few talented assistants can help with gigantic canvases and it's a sure bet that a lot of household named painters are actually painting for museums and/or on commission from clients well able to finance the horrendous fees asked for such works! But that's surely how it was done 400-500 years ago. The paintings were created by "schools", the master designing the work and adding the finer details, but with assistants to do the hard grind and apprentices to do the rest of the chores. However, in those days, apprentices learnt everything about their job on the job (learning by doing), including how to make paintbrushes, prepare supports, mix and blend paints, long before they were allowed to paint anything. There was no such thing as an art store - that paradise where everything seems possible, if only you could afford that incredibly expensive tube of oil paint..........
These days the method - in abstract painting - quite often consists of (mindlessly-mindfully?) beavering away with various implements and materials, starting with nothing, then adding and subtracting until the desired - often unplanned and therefore surprising - result is achieved.
I'm never quite sure what comes first in abstraction. It's like the chicken and egg dilemma. For example, you see a painting somewhere and it's called "The dawn of civilization", but all you can see on the canvas is some rather untidy surface work and a squiggle or two. There may be a bit of newsprint stuck on, or a fingerprint, or a handwritten line of wisdom, or a photo of someone's ancient relation. So did the artist decide on a title and then try to express it on the canvas, or did he splash and smash away at the canvas and then discover that what he had done was parallel to the dawn of civilization? No way of telling, even by asking the perpetrator!