Maki has trouble making friends because she’s afraid of being used.
In the OVA, we see her as a cheerful—possible even mischievous—child. Assuming that this is what she was really like as a kid, she was probably still pretty naive about the crueler realities of life: most relevantly, the consequences of being the heir to a renowned hospital chain. Her peers probably know her as the Nishikino child—so, oh, she must be rich! Smart! People are generally always nice to wealthy/resourceful people, because predictably, they’ll want to find a way that wealth to trickle down to them as well.
Through years and years of peers pestering her for “Oh, Nishikino-san, what’s the answer to this problem?” or “Nishikino-san, can we have a party at one of your five vacation homes?”, she becomes increasingly cynical and bitter about making friendships, and as a result, she turns into the distant and surly individual we know in the anime.
In chapter two of Nico’s SID, Maki is the only member in μ’s who has an issue with Nico referring to μ’s as her ‘stepping stones’, whereas everyone else is like nah, μ’s is a stepping stone for all of us, nbd. It also adds another layer of depth as to why Maki is so hesitant at first to compose a song for Honoka: not just because it’s a hassle, not just because Honoka is just a creepy, pesky stranger, but also because friggin’ hell,why is another person asking me for favors.
It’s not until she sees and experiences firsthand the sincerity and ambition of μ’s that she finally decides to open up to people again—and not just to anyone, but to eight other girls who have absolutely no ulterior motive for being friends with her.