Well, that’s an easy one to answer.
President Obama was a nincompoop. He was basically incompetent amateur, playing at being the President (witness him begging Russia to give him more space, followed by Russia **taking ** more space, or him begging President Putin to stop hacking US elections, then proudly declaring “I’m a big boy, Russia stopped hacking our elections!”, and then **suddenly **it turned out Russia stepped up its hacking of our elections, immediately after Obama’s desperate pleas.
The same with Biden’s son story: Obama saw absolutely nothing wrong with Hunter Biden, who managed to get kicked out of the Reserves due to his coke addiction, serving on the board of the largest Ukrainian gas company. This was, of course, at the time Obama was pandering hard to Russia, refusing to impose real sanctions on Putin or provide lethal weapons to Ukraine.
Heck, I remember White House Press Secretary being asked point blank if there was not an itty-bitty conflict of interest with Hunter Biden getting paid 50K a month for a job he had no qualifications for and Vice-President Biden’s incompetent handling of Ukraine’s affairs. The Press Secretary was clearly disturbed and managed to stammer something along the lines of “Well, Hunter Biden is a private citizen, so you know, it’s kinda ok for him to be involved in Ukranian politics”. (and in Ukraine, gas IS politics).
So, to sum up the answer: incompetence, corruption and greed at Obama’s administration made them turn blind eye to Hunter Biden’s clearly inappropriate behavior.