In harry potter and the half-blood prince, how do you explain that Harry got Snape's old textbooks?

This book was given to Harry Potter by Snape on purpose, on the grounds that Snape didn't show any surprise when he found out that Harry Potter used the "shadowless front" twice, and Snape created this magic himself. "Dare to use the spell I invented to deal with me? Yes, I am a half-blood prince. " Don't you understand?

Snape gave Harry Potter the old textbook in order to improve the learning level of Harry Potter's magic class and please Lagerhorn, because Harry's mother Lily is Professor Lagerhorn's favorite student, and Dumbledore used Harry Potter to make Lagerhorn feel guilty about Lily, thus asking the secret conversation between Voldemort and Lagerhorn and finding Voldemort's weakness. According to the level of potions before Harry Potter, it is obviously impossible.

With the help of the book Half-Blood Prince, Harry won the first prize in the potions configuration competition in class, and also won Fuling potions, which became the key to Harry's success. A boy wearing Lily glasses won the first prize in Potions class, and successfully called out Professor Lagerhorn's tears and made him hand over the key souvenir mori.

I believe Dumbledore arranged all this, because if you look at the details of the whole Harry Potter, you will find that both Harry Potter and Voldemort are obviously arranged by Dumbledore from beginning to end. As for investigating the secret of Voldemort's immortality, Dumbledore can't rely entirely on Harry Potter's efforts. He must have paved the way for Harry at the critical stage. In fact, Harry Potter accomplished a series of achievements from one to seven with the secret help of Dumbledore. Snape is Dumbledore's right-hand man.

So from the attitude of Snape and the children to this textbook, we can also see why Snape is a master of potions and dark magic, but they are not, the gap between learning tyrants and learning scum. Yes, in terms of knowledge and talent, Hermione can only be regarded as a better level among scum for Snape. Snape has a special research spirit, like a professor and tutor engaged in research in a university, Hermione is more like a junior researcher specializing in application, and Harry and Ron are probably scum football players who can't graduate smoothly in Snape's eyes.