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Try playing the F chord with a capo on the first fret to see if it's any easier. If it's easier with the capo, you may have nut slots that need to be filed a little deeper. It was just a thought I had, since I one time had the same problem with one of my guitars. Once the nut slots were correctly set, the problem was gone.
Remember that a barre chords doesn't bar all six string but only frets the strings that aren't fretted by the other fingers. Concrete example: An F chord is 133211. The first finger presses ("bars") only the sixth, second and first strings. So fret the sixth string like you normally would with the tip of your first finger, then lie your finger on that same fret so the side of your finger catches and presses the first two strings as well. No need to put pressure on the third, fourth and fifth strings (133211). That would waste energy and make your hand unnecessarily tired. Another way to describe this is your bar finger is ever so slightly rounder that the radius of your fretboard (pushes only on the outer strings. This applies less in the case of a minor seventh chord with the root on the fifth string like a Bm7 x242322 but you can worry about that one later).
additional note: Put no more pressure than is needed to do the job and try to "feel" with the side of your finger, if you press like crazy and it still doesn't work on some strings, chances are you are pressing way too hard on some strings and not enough on those that still rattle for lack of pressure.
You could down tune your guitar a half step and capo on the first fret or even a whole step and capo on the second fret. This would reduce string tension and the nut is now essentially the fret so it's lower also.
There are substitute open chords that can be used instead of the barr chords though not always suited in some cases.
Much good technique advice here. In my experience, it was very liberating to begin to use "power chords" a few years ago in lieu of barres, when possible. I don't like barre chords--either the act of making them or the way they sound. Certain power chords allow some unfretted strings to ring out as "drones", rendering a much fuller sound on an acoustic guitar. Try, for example, 079900 for E (actually E5 I guess, because no third). I love that chord and use it a lot. Also x07650 for A.
Generally, I avoid barres whenever possible on acoustics, but use them more often with electrics.
She's the lady of the light
Yellow incandescent night
Tiger eyes burning bright
In the understory
I can't see the forest
For the branches and the leaves
But I believe
I do believe
"Music is your own experience, your thoughts, your wisdom. If you don't live it, it won't come out of your horn."
Look, barre chords are simple. Your finger is the nut, if your guitar is poorly set up, it's near impossible for someone new to engage that. But as said, with a WELL SET UP GUITAR, it's heaven, and you need to learn heaven, or switch to saxophone.