The reason that he would not look into it is because of corruption in the appearance of corruption. In general, the president does not engage in activity related to individual criminal case. The reason is that the ability to prosecute someone is incredibly powerful. If we left that in the hands of a president, who has immense political motivation, then they might abuse. The fact that the person in question is Trump's main political rival, who polls show would beat Trump by 10 points or more, gives him even more motivation to abuse his power the idea that this was some sort of legitimate action is totally blown out of the water by the fact. For example, Trump did not ask about any other corruption cases. He wasn't concerned, for example, with Shady business dealings in Ukraine by his personal lawyer Rudy Giuliani. Nor was he concerned about the potentially corrupt or illegal actions of anyone, weather Ukrainian or American, other than Hunter Biden, the son of his rival. This shows that it's not a legitimate good government attempt by Trump but an attempt to influence an election.
I think that a lot of trump supporters suffer from a situation where they are willing to excuse a lot of behavior from Trump because they agree with him politically, and or disagree with his Rivals. So let's turn this around and ask about the opposite. We don't even have to go into a hypothetical here because Trump himself has accused other people of doing to him precisely what he was trying to do to Joe Biden. I'm talking, of course, about the Russia investigation. Donald Trump's Narrative of the Russia investigation is that it was a complete hoax from Soup To Nuts. Now there's obviously some evidence on which to build an investigation into Trump's connections with Russia. After all, one of his staffers did know about the hack into the Democratic party email system before that became public. There were numerous contacts between people in his campaign and Russian agents. And Trump did often act in ways which raise the suspicion that he may have been engaging in a quid pro quo with Russia. But, none of this ultimately Rose to the level of criminality and Trump has claimed that the entire thing was a politically motivated attempt to destroy him. In the narrative spun by Trump and his allies, the Obama Administration, and or Democratic operatives within the federal government, as well as other Trump haters all conspired to create this investigation in order to bring Trump down because of politics. This is the exact, I repeat the exact, same thing that Trump is doing to Joe Biden. He is trying to instigate an investigation against Biden not based on the evidence, but based on his political rivalry with him. If, As Trump claims, it's not acceptable for people to have investigated him for alleged ties to Russia because they were motivated by politics then it's not okay for him to try and investigate Joe Biden because of alleged wrongdoing in Ukraine. You can't have it both ways