Why are football players accompanied by kids, while walking out at the beginning of a match?

There are many reasons, and I'm sure many have their own opinion, however, given my sports background, I strongly believe it is a form of promotion. Promoting good sportsmanship. Promoting fair-play. Promoting a healthy, and competitive attitude. 

The players are role models, and are looked up to by many young pupils. It's important to teach kids from a young age that sports is a competitive activity but being a good team player is key. Sometimes you win, sometimes you lose, but you are always expected to show good sportsmanship and respect your competitor.  

It is also a form of public relations, community involvement. But that's a given considering it's a business after all.  Hope that answered your question!

to inspire the new players

It signifies that football is a game for everyone (no critism), it also signifies oneness, fair play and love for the game