if p, then q is not equivalent with if q, then p. However this follows: if ~q, then ~p. It's not raining, it must not be my birthday.

It's more like:

"It only rains on my birthday. It's raining today - it must be my birthday."

At least I'm not aware of any inversions of the 10-2 bond yield curve in the last 50 years that was not followed by a recession, however minor.

There have been inversions in the X - Y bond yield curve in the last 50 years that were sometimes followed, and sometimes not followed by recessions.

You didn't come to the number 10 - 2 independently. It was cherry-picked to fit the narrative.

The other ratios have inverted over the last 6 months, I think as early as the 5-1 ratio in January. The 10-2 is simply the more extreme indicator and the bigger signal that a recession will probably happen in the coming 12-24 months. I used 10-2 both as it is in the news this week and is the critical indicator that I studied in college. In January I was referencing the 5-1 as an early indicator that without correction would lead to the 10-2 inverting as well.