Filch is a Squib. And yet, he has a Kwikspell letter in his office. Ron defines a Squib as "someone who was born into a wizarding family but hasn't got any magic powers." Isn't the Kwikspell course just a waste of time? Surely he's noticed over all of the time he's been doing Kwikspell for, that it has no results? Why is he still on Kwikspell?
There might be two reasons which I see:
- Squibs in the wizarding world still believe that they can get up to speed with magic through those quick and simple courses
- As Megha said in the comments above, it must be a scam which made the Squibs in the magical world convinced that magic can be learned even if you were born with zero magical powers
From a Pottermore article:
The proud old warlock went further: a Squib in any family was a sign that they were in decline and deserved to be winnowed out.
So, it is pretty much evident that Squibs can't get up to speed with magic and they are destined to live as magically handicapped people.
So, the Kwikspell thing must most probably be a scam.
Filch hadn't actually started the course (or had only been using it for a short amount of time).
The question presumes that Filch had been using Kwikspell for a prolonged period of time. I don't think that's true.
The Kwikspell excerpt that Harry reads sounds much more like a promotional blurb than the course itself.
A Correspondence Course in Beginner's Magic
Intrigued, Harry flicked the envelope open and pulled out the sheaf of parchment inside. More curly silver writing on the front page said:
Feel out of step on the world of modern magic?
Feel yourself making excuses not to perform simple spells?
Ever been taunted for your woeful wandwork?
There is an answer!
(Chamber of Secrets, Chapter 8, The Deathday Party).
And so on. It doesn't sound as though Filch has the full course at his disposal. It sounds more like he has the promotional brochure which is sent out to prospective customers.
That's not to say that Filch had definitely not started using Kwikspell. The envelope Harry sees also contains lesson one from the course itself.
Harry was just reading 'Lesson One: Holding Your Wand (Some Useful Tips)' when shuffling footsteps outside told him Filch was coming back.
(Chamber of Secrets, Chapter 8, The Deathday Party).
Nevertheless, I think it's fair to say that Filch didn't have access to the whole course. Kwikspell would presumably have made its money by sending out one lesson a week in exchange for payment, rather than giving their customers all the lessons in one go. That would be the customary approach for a 'correspondence course'. They probably included lesson one with the promotional kit to give prospective customers a flavour of the course and hopefully encourage them to sign up. All this means that Filch wasn't an experienced Kwikspell user. He had only reached the first lessons - and may not have started the course at all. It's quite likely that he was still weighing up whether or not to sign up for Kwikspell when Harry found the letter.
Since Filch was a novice when it comes to Kwikspell he has no way of knowing whether it works. He only has the word of the promotional parchment to go by. If Kwikspell was a scam then Filch wouldn't have known.
We know that Filch is still a Squib three years later. Whether this is because he gave up on Kwikspell, because it didn't work for him or because he never took it up in the first place (due to the turmoil involving Mrs Norris) isn't clear.
"Don't stun them, Filch!" shouted Umbridge angrily, for all the world as though it had been his incantation.
"Right you are, Headmistress!" wheezed Filch, who as a Squib could no more have Stunned the fireworks than swallowed them.
(Order of the Phoenix, Chapter 28, Snape's Worst Memory).
It also isn't clear whether Kwikspell really is a scam or not. I'm inclined to think it isn't - there's no reason why remedial lessons for people who didn't excel in school for whatever reason wouldn't be effective. As a Squib Filch may have been a poor fit for the course. Kwikspell was aimed at people whose magic is subpar rather than non-existent. Filch was probably considering applying for it out of desperation.
Filch likely hoped it would make him become magic.
Filch presumably wanted Kwikspell to try to become magical through using it. However, J.K. Rowling stated on her website that it never worked.
Squibs would not be able to attend Hogwarts as students. They are often doomed to a rather sad kind of half-life (yes, you should be feeling sorry for Filch), as their parentage often means that they will be exposed to, if not immersed in, the wizarding community, but can never truly join it. Sometimes they find a way to fit in; Filch has carved himself a niche at Hogwarts and Arabella Figg operates as Dumbledore’s liaison between the magical and Muggle worlds. Neither of these characters can perform magic (Filch’s Kwikspell course never worked), but they still function within the wizarding world because they have access to certain magical objects and creatures that can help them (Arabella Figg does a roaring trade in cross-bred cats and Kneazles, and if you don‘t know what a Kneazle is yet, shame on you).
- Squibs (J.K. Rowling’s old website)
This was likely only because of Filch’s own hope that something might work. The Kwikspell course was marketed to unskilled wizards - it never claimed to be able to make Squibs magical.
“Feel out of step in the world of modern magic? Find yourself making excuses not to perform simple spells? Ever been taunted for your woeful wandwork? There is an answer!
Kwikspell is an all-new, fail-safe, quick-result, easy-learn course. Hundreds of witches and wizards have benefited from the Kwikspell method!”
- Harry Potter and the Chamber of Secrets, Chapter 8 (The Deathday Party)
Therefore, it seems likely that Filch most likely wanted to take the Kwikspell course in the (misguided) hope he could coax some magic out of himself, which does not seem to have been encouraged by the advertising of the Kwikspell course.