Peachey's right. There's another expression, "to give someone the boot." It means to fire someone/give someone the sack/get rid of them. Example - "Mr Smith is always late for work! We'll give him the boot." (Oh dear, Mr Smith is going to become unemployed) Another example - "I don't like my girlfriend. I'm going to give her the boot." However, I don't think this is the sort of boot that you mean. A FRIENDLY boot is different from THE boot ! So Peachey's explanation says it all.

Are you sure you have the right expression? If you "give someone a FRIENDLY boot", that means you admonish that person, but in a way that will be helpful and motivating. Here's a sentence I found online (corrected): "I really meant this advice as a friendly boot, to kick you in the butt and get you moving."

give someone the boot (transitive, idiomatic, UK, informal) To fire, to sack, to dismiss. I am sorry for your husband and children, but I have to give you the boot. They said I couldn't do the job so they gave me the boot. So, now I'm looking for work again.