The person you are debating has made a definite claim here, that things are not improving under democratic leadership. This isn't necessarily true in the first place, if you compare UE rates over time from democrat-led cities to republican-led ones. A line of questioning that allows you to find and look at data that is new to both of you is invaluable. Shared learning experiences are a powerful thing. Make sure to compare relative white vs black UE rates as percentages.

Cherry-picking Obama's first two years out of his entire presidency is obviously something that was fed to this person. A line of questioning that leads to the dismissal of extenuating circumstances (the pandemic unemployment rate vs the post-2008 crash rate is a good example) will allow for a better comparison. This could lead to convo about how slow economic change is, and an opportunity for data-driven discussion of R vs D administrative acumen.

In any case, the consistency of high black unemployment over time leads to an overarching societal problem, not a politically-driven one. Simple googling for black vs white historical UE charts can show that.

Hope this helps!