Tips for fitting garden hose on tight hose fitting/quick connector
This is possibly a daft question, but just to be sure - you are unscrewing the "nut" that is on the right side of that picture, sliding that over the hose, pushing the hose under the "fingers", and then doing the nut back up? 

If so, and you're sure that that hose and fitting are the same size, then try putting the end of the hose in a bucket of hot water for 15 minutes. It should soften the hose enough to allow you to wiggle it all the way into the connector, and then do the nut up.

Edit: as they say a picture is worth a thousand words. This clearly shows what I'm trying to explain.

https://www.youtube.com/watch?v=HR8OkhLhtYo