Also, there's basically one way to differentiate (not really, but kind of) wheres integration is so tricky there are many, many ways to do it.
There's a reason it was developed first, historically speaking.
Learning should be like peeling onions. You peel off one entire layer, from all sides, before moving on to a deeper layer of complexity.
By the time you know about drawing lines on planes to find the integral area underneath, you've already figured out the derivative so you know what direction to move your pen in next while drawing the line
I think these are actually pretty abstract, so it's hard exactly to grasp what a derivative is until maybe Calc II or III -- imo, the main problem is that it just seems like mathematical black magic: you need to define a limit, you need to use that definition to subtract two slopes, the complexity of which magically kind of vanishes, and you end up with a "method" for spitting out derivatives. Whereas finding area under a curve seems like a common sense thing to do: you take smaller and smaller slices of a thing and add it all up.
I do agree that if you really learn anti-derivatives (which, by all accounts, is harder), you basically get derivatives for free.
Curiously his book on mathematical analysis is excellent, except that many of the exercises were downright wrong.
For many students, intuitively understanding the infinities and infinitesimals in integral calculus come easier than those in differentiation.
That book was widely used at Caltech, MIT, and several other top schools for decades.