Giffen good: why does consumption increase with a price increase?

If I am not mistaken, the negative income is greater than the substitution effect, so the net result should be a decrease in consumption. The explanation I am reading says: "the negative income effect of a price decrease outweighs the positive substitution effect, so that a decrease (increase) in the good’s price has a net result of decreasing (increasing) the quantity consumed."

I understand (I think) how a decrease in price has an effect on quantity connsumed - the more free income a person has, they less likely they are to spend it (after the substitution effect is taken into account) on a less desireable good, but why would an increase in price lead to an increase in consumption? That sounds more like the charicteristic of a Veblen good, but with a Veblen good you’re often spending more for a label or the perception of quality/wealth/status, etc. What is the deal here?

Imagine a family that subsists primarily on rice, but with some meat occasionally. If the price of rice were to rise, they can no longer afford both rice and meat. Their consumption of rice increases, and their consumption of meat decreases. Rice is a Giffen good (in this scenario).

Thanks. That makes perfect sense now. As always, thank you for your continued help.

My pleasure.