Expanding on Leon The Professional, I think looking at the personality of the characters helps explain those deleted scenes. Leon, despite being a very proficient killer, is also bound by honour and is in some ways socially and emotionally naive. He doesn't display the worldliness of Gary Oldman's character; he has a kind of purity which makes him more like a child than adult. He talks about how he wants to give it all up, to enjoy simple things like sleeping in a bed rather than sitting in an armchair with a loaded gun beside him. His employers mostly exploit his ability to kill and don't give him emotional kudos, whereas he finds a strange and socially worrisome connection with a young girl. He becomes her ward and protector after the death of her family.
Matilda is different. She shows herself to have maturity, from her presence of mind in walking past her family's apartment and going to Leon's door, but is still at that grey area where teenage girls find themselves in an innocent puppy love, but don't know how to handle it. So they behave in silly ways to emotionally engage someone, attempting to mimic what their uninformed perspectives think will work. She's also in the position of being attached to someone who saved her from a traumatic situation.
There's a lot of nuance to the characters of Leon and Matilda, now that I think about it. The international and US cuts of the film removed the scenes of emotional connection, likely because it would offend someone. In today's political climate, it would be even worse.
My fave sequence in that movie is where Jean Reno hands Gary Oldman something, dies, Oldman opens his hand, finds a grenade pin, opens Reno's jacket, sees the grenades, goes "Sh it!" and goes kablooiey.
