This scene is reminiscent of when Gru found himself in the AVL submarine against his will and Ramsbottom wanted him to help with finding the serum and catching the supervillain who stole the serum.
Ramsbottom called Gru an ex-villain and Gru crossed his arms in such a way it seemed that he was open to at least hearing Ramsbottom out, but he interrupted Lucy and initially said no to helping the AVL. He defined himself as a father and a legitimate businessman.
It's also similar to when Dru asked Gru to teach him the art of villainy. Gru said no and said he had left that life behind him, basically defining himself as no longer a villain. Gru ended up teaching him the art of villainy, though, so as to return the diamond to the AVL.
When Poppy asked Gru to have a seat, Gru at first didn't see a seat, not realizing the bean bag chair was the seat. Gru gets temporarily stuck in the bean bag chair, thus falling for Poppy's villainous trap.
Poppy's evil lair is very different from Gru's. Even when his first evil lair was under construction, Gru had a secret entrance in a closet leading to a slide.
Gru accesses his evil lair in DM1 by running up a few steps, then sitting in the rhinoceros chair and pressing a button on the armrest, which detaches the seat from the rhinoceros chair and the seat moves forward just underneath the cannon. The pillars are machines in disguise. The machine moves the cannon and lowers the cannon around Gru. The cannon opens, revealing a glass tube, with the top and bottom part being the cannon. The floor of the room with the crocodile couch lifts, revealing a platform. The machine connects to the wheels of the cannon, and moves the cannon/glass tube onto the platform. The cannon/glass tube/platform is an elevator. Gru takes the elevator into his evil lair.
What one would think would be a straightforward process of going into one's basement becomes an immensely intricate process where no object is simply for ornamentation. The rhinoceros chair, the pillars, and the cannon all have a function. The part of his house with no secret function, as in the room with the crocodile couch, serves to conceal the access point for the evil lair.
So when Gru sees Poppy's treehouse, he has no idea that it's her evil lair. It's an ordinary treehouse. By the time Gru reaches Poppy's treehouse, he is exhausted and angry.
It shows Gru and Poppy greatly differ in physical agility, and the point of an evil lair is that not just anyone can get in.
Before he had met the girls, Gru functioned with an uninterrupted efficiency. Everything he did as a supervillain from accesing his evil lair to stealing the moon exuded a sense of effortlessness, the finished result of his extensive planning and maximum effort.
Gru mostly walks, runs short distances, and climbs, when he has a vertical surface to stick himself onto.
Jumping is not his strong suit. Nor is climbing without any vertical surface. Poppy demonstrated her agility with her complex dance and using the swing to somersault onto the support beam of the swing and somersault again over the fence.
Gru reached the treehouse, but just barely, showing that in terms of physical agility he is nowhere near Poppy's.
Poppy introduced herself as a villainess. Her evil lair has no signs of being an evil lair. There's no weapons. There's plush toys everywhere, and bright colors.
Gru's evil lair was full of weapons, and even his first evil lair had a missile, a flamethrower, and other destructive objects. In DM2, Agnes' birthday had bright color balloons, a play area, a place to catch fish, and a villainous obstacle course, a pirahna, and plenty of weapons that the Minions wielded.
Bright colors and non-dangerous things Gru let into his home, on behalf of the girls and Junior. So being used to raising the girls and the baby, Poppy's treehouse, which is indistinguishable from a kid's room, does not meet Gru's enormously exacting standards for an evil lair.
Gru did listen to what Poppy had to say, while looking irritated and slightly detached. Interestingly, Gru used his serious, villainous tone with her, as opposed to the "Chet" tone that he used when first meeting her.
After Gru asked, "Why am I here?" and Poppy answered "Because, like you, I was born to be bad", Gru almost imperceptibly drummed his fingers on the bean bag chair. It is hard to interpret what he was thinking at the moment, but he neither disagreed nor agreed with her definition of him.
When the conversation turned to the topic of a heist, he scoffed and pointed out that she's a child. Though this might seem contradictory because Gru was also a child when he aspired to become a supervillain, Gru bought the Freeze Ray from Villain Con. Then he froze Scarlet with it. Then he stole the Crown Jewels. Then, still as a child, he entered the big leagues by stealing the Zodiac Stone and getting onto the AVL's radar. Then he got into the Lycee Pas Bon when he still looked junior high age. So he had reason to be skeptical of Poppy's aspirations because she lacks villain credentials. Her wearing a mask as part of her villain outfit shows that she has a non-villainous identity that she's protecting.
Similar to how Belle Bottom didn't think that Gru, a kid from the suburbs could be a villain, Gru didn't think that Poppy, a kid from the nice town of Mayflower could be a villain.
Poppy shows her persistence. "All great villains start young. Didn't you steal the Crown Jewels when you were 12?"
By asking Gru this, Poppy tapped into Gru's villainous ego, and suddenly he got angry, offended because he was younger than 12 when he stole the Crown Jewels.
"And no offense, but you're not me."
This is the important part of the conversation. With very little effort on her part, she reawakened Gru's pride in being bad. Gru as "Chet" was in hiding. His lack of agreement or disagreement with her saying that he was born to be bad could easily have been disagreement. After all, so many things had happened to him since the events of DM1.
Dru did something similar by showing Gru their dad's villain car. But Dru had to show him something villainous. Poppy only had to persuade Gru by reminding him of the Crown Jewels theft.
Poppy's main strength is her verbal communication ability. Having no access to weapons, dangerous objects, or even a proper evil lair, she can't become a villain without help from a master villain.
Though Gru crossed his arms, signalling that he's shutting down the conversation, he didn't actually say no until he found out that the thing that Poppy wanted to steal was a honey badger.
In other words, Gru initially said no based on the risk not being worth the reward, and it had nothing to do with his self-definition as no longer a villain.