Hi Javier,
I’m relatively short (5 feet 4inches) and have pretty small hands. I too had issues with the C chord when I was in grade 1. What helped me is focusing all of my song practice with songs with a C chord in it. (I used what’s up by 4 non blondes). I now do clean C chords about 99% of the time and have 0 problems incorporating it in songs. I bet it’s just a matter of persistence and patience.
Make sure that your thumb is in the correct position (on the middle of the back of the neck) and arch your fingers as much as possible to clear the strings, my hands are smaller than my wife’s yet I can still play clean chords on a Classical guitar which has quite a wide neck, just wait until you need to play a G7!!!
Thinking that my hands were the wrong shape for guitar was what made me give up guitar the first time in my teens. It’s just not true - don’t think that way.
If you can play a C chord clean in isolation, you can learn to play it clean in songs. It’s just practice, and slowing down. Remember practice makes permanent? Try to slow the songs down, or do one strum per bar, and try to get those changes clean, if slow. Then speed up the strumming. It will come with persistence, like @alexisduprey says. And once you have it, it will be automatic.
Some chords are hard ones to learn. Some are easy. C is the first hard one - later you’ll learn other chords that make C look like a piece of cake 
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Yeah mate, it just comes down to technique and practice. You’ll get there before you know it. Maybe post a quick clip. It may illuminate something that the folks here can help with.
Re the small hands query, there’s plenty of 6 years olds on Youtube shredding it better than all of us with their tiny mitts. 
Cheers,
Shane
I’ve got long fingers, and am still not happy with my C chord changes, after working on it for several months now.
Made worse because I had to give up on muting the big E string with my ring finger, and switch to thumb muting. Feels like I’m starting from scratch, and can be quite frustrating.
As others have said, posting a video would be a really good idea (this is definitely a case of “do as I say, not as I do”…I haven’t posted one on my C chord struggles either :()
On the other hand, nobody picked me on the C chords in my Behind Blue Eyes video, so I guess they sound OK to the listener. But they don’t feel good to play.
Been working on it… Still not “perfect” but much improved. The app is really what’s been keeping me going, actually.
Well done Javier, perseverance always come through. Couldn’t agree more with your comment about the app, it’s a god send!
Are you doing the module 4 finger stretches ? If not you should be as it will expand and open up your ability to stretch.
https://www.justinguitar.com/guitar-lessons/beginner-finger-stretches-b1-401
As my fingers, well at my age, my whole body gets stiff and tight. I still do this as a daily warm up but start at the 7th fret and work down to the first. I have a number of songs that have a 4 fret span and always struggle if I approach them cold. This exercise opens things up and for sure back in the day made the C chord more doable.
Oh I have small hands and fingers, Or at least I think I have.
My 2 cents
I actually do those stretches, maybe not as religiously as I should. I play daily, but 3 or 4 sessions are actually “formalized” practice. The others I’ll head up to my office for something else and end up spending an hour playing songs on the app. Lol.
Wife thinks I’m funny.
Mine thinks I am certifiable !! Make those stretches part of your daily warm up before playing. It will make a big difference. Just a few minutes doing those slow and deliberate stretches will make a world of difference. All about discipline.
@chubbyfingers, I see @stitch has provided a full technical answer to your question, but I remember pondering that 1 4 5 thing myself and the answer is: it sounds good and so it’s become massively popular. Play the chords with those numbers in that order in the key of C and they sound nicer than maybe 1 2 3 or 5 1 4. As far as I can tell thus far, ALL ‘music theory’ is just the formalising of what people generally agree to be pleasant to the ear!
Richard
It sounds good and familiar as 1 4 5 is the bedrock of every 12 Bar Blues.
I can do the chord perfect for C chord pretty well. But when I’m doing one minute changes i often find that my index finger (on the 2nd string of C chord) is getting muted. I don’t seem to have sufficient finger strength right now to keep the index finger pushed down the whole time hard enough for the note to ring clear. Also some of it maybe because when I’m doing the changes the finger position and angles change. Any help on this please.
Just keep at it Anshul, you’ll get there 
Try to pause the odd time when it’s not ringing out true and adjust your fingers until it’s a bit better, doesn’t have to be perfect each time, that will come…
Hmm, index finger is first fret. Do you have the index right up close to the fret? If you do, and you’re still having to use a lot of pressure, you might have a high action on your guitar which would be making it hard to play.
Are you able to easily fret that note if you just fret that one, and ignore the rest of the C chord?
Are you playing acoustic or electric, and what gauge strings do you have?
I am going to assume you mean your middle finger on the D (4th) string second fret (E), since that is the way Justin teaches and how I can relate with a similar problem.
When my index (B string first fret) and ring finger (A string third fret) press at the same time, my middle (longest) finger on the D string second fret (E) automatically lightens up and I don’t press that note well. Sometimes the index finger also leans a little into the D string, or the middle leans on the G.
I have just recently brought this to my own attention (finger style has a way of pointing out such lapses) and am working on it with attentive and remedial practice. It also helps to look at how you arc your fingers around to reach the notes. You may need to move your wrist a touch forward or more likely bring the palm of your left hand up towards the bottom of the neck.
I still find the C cord a stretch with a long scale guitar.
As someone already suggested, it might be the action of your guitar. It’s a fairly common problem to have difficulty getting strings to ring in the first fret, often because the nut is too high.
Is there any objective way of knowing if the action of the guitar is high or if it is correct.
