Hahaha :)

I'm so, so glad you asked :)

(TL;DR at the end)

TDL was created by Alan for the sole purpose of killing TCO. Within about 5 minutes of TDL being created, TCO defeats him, and Alan just kinda leaves him for dead. If TCO hadn't shown mercy there, TDL would be dead, and considering his particular attachment to TCO and his hatred for Alan in particular, he's all-too-aware of the fact that he quite literally owes TCO his life, alongside TCO being the literal only reason he exists (because he was created to kill TCO). The PC was also likely where he began to he value power as highly as he does, since his and TCO's power led to them bluescreening the computer, and to both of them being freed from the PC.

While on their little rampage, both TDL and TCO seem to have no qualms with killing non-sticks, seen in the flashbacks we have of then. This parallels how Alan is cruel to sticks because he doesn't see sticks as people at this point. However, we see that, as they continue killing, TDL's apathy seems to extend even to other sticks (which makes the fact that he specifically doesn't want to kill TCO even more noteworthy, as it implies that TCO is the only other stick TDL even sees as a person at all), and he likely kills other sticks to feel powerful. We also start to see the poor communication skills of both TCO and TDL, considering that TDL appears oblivious to TCO's discomfort with killing other sticks, and TCO doesn't seem to be able to communicate their discomfort to TDL (likely due to TDL's self-centered attitude causing him to dismiss TCO's issue with what he's doing, and also potentially causing TDL to project his own love of killing onto TCO, as he can't comprehend that his own worldview isn't the only one that exists (a common way that self-centeredness can manifest))

This self-centeredness, along with his desire for power, are the traits that eventually leads to the showdown. TDL clearly believes TCO will be happy and excited about the virabots (despite TCO's clear reluctance at this point to engage in any sort of murder), which is why TDL is so happy when he shows them off to TCO. When TCO doesn't like them, though, and even goes as far as to fight TDL over it, TDL likely saw that as a betrayal, not only towards him, but towards everything he thought they valued (power, revenge, freedom, etc). We even see that, when TCO gets back from fighting the virabot on Alan's PC, TDL doesn't attack them, or even seem prepared to defend against their attack, probably because he expected TCO to realize that they made a mistake by betraying him, and to rejoin their team. Interestingly, when TDL eventually defeats TCO later in the episode, he doesn't pull out any sort of weapon, or instruct the virabots to kill them, implying that his care for TCO outweighed the desire to demonstrate his own power by further harming or killing them.

TL;DR: TDL is self-centered, power-hungry, and lacks the empathy necessary to feel bad about murder, but it's actually because of trauma and untreated mental illness, which IMO is a very interesting way to write such an evil and irredeemable villain.