Why?

Of course words change meanings over the centuries. Lower case paganism, is not in my English. Paganism (Capital P) is the noun. Pagan, may well have come from Latin; but it is now an English word and it means "unbeliever,infidel"-- Oxford English Dictionary.
Nice once meant "exact", now it means "good". Hardly anybody writes, or speaks, true English. Even the word Hamburger has become Beefburger for some strange reason!

In my belief, since i'm Christian. I say and fully believe Satan is a horrible deity that whether pagan, or not, shouldn't be worked with.

Satan is the trapper. He'll use temptation, secrets, and your greatest weakness's against you!

Well I have to say that both you are right about the word usage of the word Pagan. But in the subject of calling Satan its no different then calling a God you follow. But calling a Deity and demanding something from them or not thanking them for their presence could have the same consequences that you believe to be true of summoning Santan. Personally i do not follow that path but it's a personal choice

Because to his followers, he is a martyr, protector and a powerful loyal ally and a savior. 'The light in the darkness.'

Martyr? No.

The simple question was WHY WOULD SOMEONE WILLINGLY INVITE A DEMON INTO THEIR HOME?

And please stop arguing over what Pagan means as that is bumping the topic.

Satan is a powerful demon who can get a lot of things done quickly and is easier to persuade than some other dietys. Because of this, people call upon him to do some of their tasks ( such as robbery or murder) because Satan won't care if he does it, and the people don't want to get caught. So in a way, he is neutral. He just doesn't care if someone asks him to murder or steal or do some other crime.

Shadowpool, please don't write your beliefs as though they are fact. Satan is a belief, not a fact.

Demons do give blessings and protect you from other demons and it does take a certain kind of person to successfully keep one. If that does not answer your question I don't know what to tell ya

Animal. People have told you your answer. To a Christian to let a angle to live in their house and get protected by it would be the greatest thing, to a Satanist It's the same thing, but with demons. Every one has different belifes. You see Satan as a evil being and many others, but some people believes he is a good guy. You should to research about Satanism and many other religions to understand why they believe in what they believe.