Curate, connect, and discover
Since the Warners had been without parents for god knows how long, Yakko obviously stepped up and became his siblings' provider. However, since all they've ever had was each other, he became really protective of them and would glare down and avoid anyone who even looked at his sibs. With this in mind, having to let them go to one-on-one meetings with Dr. Scratchansniff and then leaving them to go to those meetings himself left him angry and incredibly paranoid, despite covering it up with his comments and shenanigans.
Fortunately, after a while, Yakko started to realize how close his siblings and even he was becoming with Scratchansniff. Even if the Psychiatrist was being driven up the wall constantly, he would always be there for them if they needed him to be and even when they just wanted him to be like when he would take them all out and just let them be kids without ridiculing them, or standing up for them to Plotz. Yakko believed that he truly cared for them in a way no one else had, which meant a lot and helped him let his guard down and trust him with the only family he had left. Hell, it made Yakko open up to him more, even confiding in him sometimes. And it used to make him jealous but he knew his siblings did too.
And as strange as it sounds, Dr. Scratchansniff was kind of like a father figure to them, as they were like the children he never had. It was an unspoken thing but deep inside they all could see it and knew it to be true, regardless of what anyone else would say.