The F chord was my most daunting challenge the first time I picked up a guitar. Don't blame your fingers just yet. A lot of guitar playing is between your fingertips and your brain. The way I learned was to just try to get sound from the first two strings. Try to just play the F and C for awhile before adding the A and F.
Try to find the arm, thumb, finger positioning that works and play one string at a time to hear them ring out. You may only need the tip of your finger to hit the C. Then practice changing from an F to say an A minor. Your brain and fingers will remember the positioning with a little practice. It all comes together at some point and then you look back and wonder how you could have ever thought it was difficult.
Difficult it trying to type after you just put down your guitar. Yikes!