Flattening of yield curve & option price

Why does a flattening of a yield curve result in an increase in the price of an option?

If that doesn’t make sense… how do yield curve shapes affect option prices? (Context of callable/puttable)

Heads up that I don’t think you can say that flattening of the yield curve will always result in an increase in the price of an option; generally speaking the price of a call option should increase when interest rates increase, while the price of a put option should decrease with such a rate increase (positive vs. negative rho). In reality changes in interest rates have a relatively small impact on option pricing - rho doesn’t get much love when you read the Black-Scholes section in the text. Similarly if your job ever sees you using commercial or bespoke software to price out an option you’ll see that your rate inputs generally don’t move the dial too much.