Why is Matthew Cuthbert so freaking loveable? He first comes off as harmless—comical, even—because of his fear of little girls. But in a town full of characters with opinions on how children should behave, we can't help falling for Matthew's simple, immediate, and constant love for Anne.
The Cuthberts aren't a chatty bunch, Matthew especially. His dialogue's usually less than a line long, so we mostly learn how he feels from the narration. But his quietness perfectly complements Anne's chatter, and when Anne asks for his opinion, he always supports what she has said.
Like Anne, Matthew has a stubborn streak. We're told that,
Argument was not his strong point, but holding fast to his opinion certainly was. (19.25)
From the beginning of his drive home with Anne, he decides he cares about her and there's no changing his mind. He makes it clear without how much he wants to keep Anne via longing looks, which leave Marilla wishing he would just argue with her:
A body could answer back then and argue him into reason. But what's to be done with a man who just looks? (4.37)
Matthew's quiet strategy of sticking to his point also gets Anne to attend a concert that Marilla initially forbids. It's a good strategy.
Matthew and Anne are good for each other. Anne brings quiet Matthew into the world more. His interest in her causes him to notice things he'd never notice before:
Matthew suddenly became conscious that there was something about her different from her mates. And what worried Matthew was that the difference impressed him as being something that should not exist. (25.1)
He eventually figures out that Anne is dressed differently from her friends. While Marilla did this on purpose with the goal of keeping Anne humble, Matthew instinctively gets Anne's point of view. He simply believes there should be no visible difference between Anne and her friends.
In turn, Matthew's constant praise and support is just as important to Anne's growth as Marilla's correcting. When Anne takes her Queen's entrance exams, Matthew inspires her to work hard:
Matthew had declared to her his conviction that she "would beat the whole Island." That, Anne felt, was something it would be foolish to hope for even in the wildest dreams. But she did hope fervently that she would be among the first ten at least, so that she might see Matthew's kindly brown eyes gleam with pride in her achievement. (32.32)
His blind faith in her inspires Anne to push herself. Where Marilla lectures Anne, the goal of living up to Matthew's esteem is a way better motivator.
When Matthew (excuse us while we ugly cry) dies, we feel that loss. Hard. He was a father figure for Anne, spoiling her, supporting her, and giving her unconditional love. We're glad they had each other…even for a little while.