There is a decently objective definition of recession: two consecutive quarters of declining economic output. Most metrics of economic output tend to have high degrees of (positive or negative) correlation: GDP, (un)employment, etc.

The issue is that what you've seen since the pandemic started has been basically insane macroeconomic statistics that defy historical correlations, so whereas the US GDP declined in Q1 and Q2 of this year, there weren't corresponding declines in other statistics (e.g., unemployment stayed low). If half of the economic indicators are signalling "recession" and the other half are signalling "rip-roaring growth", any definition that pigeon-holes the economy into one or the other is likely a bad definition.