How does Bitcoin protect against inflation? In an economy where the prices of goods keep inflating, like a car going from $10,000 to $20,000 in 1 year, what would be the incentive for people to put their money in Bitcoin? Wouldn't the price of a bitcoin stay the same or decrease because people need their fiat money even more?
Inflation is increase in price without increase in utility. A car with similar features helps you get from point A to point B just like it did one year ago (same utility). However, the cost of the car increased by 2x one year later (higher price) indicating that the currency in which the price has been quoted has been reduced to 0.5x versus its value last year.

In an economy, we have economic output and wealth generation that happens over the course of years. This is represented by increased technological progress that brings in new jobs and as a result improves consumption of goods in the economy. In traditional economics, government tends to stimulate this growth by printing money and spending it on projects like infrastructure, research etc. However, most of the times the increase in economic output trails the value of currency that has been printed. This means slightly higher economic output is now being represented by much higher money in circulation, which results in devaluation of the currency.

In Bitcoin, the supply is capped at 21M. As Bitcoin gets used in almost all of our day-to-activities, it will indirectly represent the global economic output. As technological progress increases outputs, the same number of bitcoins will represent a higher economic output every year. Thus value of a bitcoin tomorrow is worth more than what it is worth today. On a relative basis this means Bitcoin appreciates in value with respect to other fiat currencies.