How do market makers profit from the bid-ask spread when bids are almost always lower than asks?

This income comes from fact most people don't want to wait and just buy/sell on current price. While market maker is ready to wait and buys/sells on a better price. Here is a simple example:

1) MM puts

• BUY MSFT@$100 order - he is ready to buy MSFT for $100
• SELL MSFT@$101 order - he is ready to sell MSFT for $101

To simplify, imagine that he has no MSFT stocks.

2) So now customer A comes to exchange and wants to sell MSFT stock now, without having to wait, so he just sells it to MM for $100.

Now MM has +1 MSFT stock and -$100

3) After 50 minutes, customer B comes to exchange and wants to buy MSFT stock and he also doesn't want to wait, so he buys it from MM for $101

Now MM has 0 MSFT stocks and $1 profit.

This is strongly simplified version of MM, but main idea is like this.

Your fundamental understanding is correct. The problem is that you're just not connecting a few of the dots.

Consider your airport currency exchange. Think of it as 1.32 CAD is the bid and 1.33 CAD is the ask. The exchange booth is the market maker. It is buying at the lower priced bid and selling at the higher priced ask. It has a lock on the market and if you excuse the expression, it is printing money. The more people who convert currency, the more money it makes. There is no risk whatsoever in this narrow construct.

For your stock market example, just substitute the words 'market maker' for 'exchange booths' and substitute $100 x $101 for 1.32/1.33 CAD. The market maker is buying at $100 and selling at $101. For market orders, any trader who buys at the ask price of $101 is selling to the MM at the higher price and any trader who sells at the lower bid price of $100 is buying from the market maker. Similar to the exchange booth, the market maker is 'printing money'.

However, there is a big difference between the currency and stock examples. Within seconds, the stock can dramatically fluctuate in price and the MM is required to continuously quote prices at which it will buy and sell the security. Earning the spread compensates the MM for this risk. Note that any trader can become the market on one or both sides by offering a higher bid and/or lower ask price

It’s the other way around: if it’s $100 bid and $101 ask the MM is asking for $101, i.e., offering at that ask price.

For example, they will say: "you can sell us 1 USD for 1.32 CAD, and you can buy 1 USD from us for 1.33 CAD". From the perspective of the customer, the ask price fixed by the currency exchange booth (1.32 CAD) is lower than the bid price (1.33 CAD).

You have it backwards. 1.32 CAD is the bid price (the advertised price at which the booth will buy 1 USD) and 1.33 is the ask price (the advertised price at which the booth will sell).

Suppose the highest bid is $100, and the lowest ask is $101. The market maker will make a loss by buying at $101, and selling at $100.

Same here. If the highest bid is $100, that means that the market maker (or someone with a competing bid) is buying at $100. If the lowest ask is $101, then the market maker (or competitor) is selling at $101. With each round trip, the market maker buys at $100 and sells at $101, making a profit of $1.