Minerva wants someone.
It's Hagrid. She knows Alb…Professor Dumbledore respected and trusted him. She does the same but….
She wishes she could just go to his little cottage and pour out all her insecurities. All her doubts about being the headmistress of Hogwarts. Of missing Professor Dumbledore.
That would be improper. Hagrid has already done so much tonight and surely needs time to rest and mourn himself. She push her own problems on him. Not now.
That doesn't stop her from wishing she could. Hagrid is an old friend of hers. They've had their disagreements, each has wondered about the other's frame of mind, but they are friends. She uses her wit to help him out of various scrapes, he uses his good nature to put her at ease when she's troubled.
Professor Dumbledore's funeral is tomorrow. The school is a mess. Minerva is a mess. Only the portraits of past headmasters see it, but she spends the night sobbing. Hagrid comes to see her in the morning. He's a mess too.
He wipes his eyes and blows his nose on a handkerchief he embroidered himself before telling her she is needed. He says Hogwarts is lucky to have her, she's such a strong woman. They need strength right now. Bad things are happening and when they do, you use your strength to fix them and make sure they don't happen again. He blows his nose again, rather loudly this time.
McGonagall feels a little better walking out of the castle. She's a strong woman and she will use her strength to make things better. In the meantime she wants Hagrid there to remind her of that.
Author's note- I think Hagrid and Minerva were close enough that they might be considered friends. There's no romantic tension, but they do seem to compliment each other in some way.