"Why would one use multiple addresses?"
Carol, the reason you would [want to] use multiple addresses is primarily for privacy.
If you use a single address, then every payment you receive and send can be [correlated] on the blockchain.
If you keep using that address, presumably all transactions produced by [it] are related to you.
You own it, therefore you're making the transactions.
If you make a transaction to any kind of company or organization that tracks your [coins],
knows who you are, where you live, or something [else sensitive] about you...
For example, let's say you buy something [online] and they deliver it to your home.
That company knows who you are because you probably typed your name into the form.
Let's say you bought some cryptocurrency [beforehand] on an exchange,
and in order to sign-up, you show them your identification.
That company knows who you are.
Now they know that address belongs to you; so does every other company they're feeding data to,
which [may be] a lot of companies.
If they know that address belongs to you,
now they know all of the other transactions coming and going from that address are your transactions.
They can pull it apart and figure out what the other addresses are, using a process of statistical correlation.
If you use a different address for every transaction, maybe one of those addresses can be identified to you,
but [then] it's much harder to identify all of the addresses and connect them to you.
It depends on how well your wallet manages security and privacy; some wallets are better than others.
There's some very interesting tricks you can do to cover these patterns of spending,
but Bitcoin isn't [very] anonymous, so you have to be very careful.
Using multiple addresses is one way you can protect your privacy,
at the very least from a casual observer, someone who is simply clicking through [a block explorer].
"f I expose my transaction ID to someone, then they can see all of my transactions."
"How does this provide me [with] privacy?"
Well, it doesn't.
If you show a transaction ID to someone, they can see which addresses were involved in that transaction.
Depending on whether you're the sender or recipient, they can look at the sender or recipient addresses,
figure out that those belong to you, and then follow other transactions that have involved those addresses.
If you want privacy [with bitcoin], [one of] the ways to achieve that...
is to ensure you only do one transaction per address, so that you don't have address reuse.
That's not easy to do.
You would [need] a wallet that supports generating a new address for every transaction.
[It should also] have some privacy features to make sure that it doesn't taint one address with another.
Using two address simultaneously in a transaction relates them.
It shows people that those addresses belong to the same person. That's not good for privacy.
You have to look more carefully at what wallets do under the covers when they construct transactions.
That leads nicely into the next question: "Which wallets have the best privacy features?"
There [used to be] an annual review and survey of privacy [in Bitcoin].
I believe it's called the Open Bitcoin Privacy Project. Let me see if I can find a link to that.
Every year that project looked at various wallets and scored them for privacy. I was one of the contributors.
You can find it at: openbitcoinprivacyproject.org (OBPP)
It scores various wallets for the level of privacy that they offer users, looking at:
whether the wallet mixes addresses together, how they handle change address,
how they order outputs within the transaction so it's not easy to determine which of the outputs is change,
whether they leave various signatures within the transaction that can identify the wallet being used,
and all kinds of things like that.
Yes, some wallets have better privacy features than others. I am not sure who the winner was last year.
I can tell you that I use Samourai Wallet for privacy. It has some excellent privacy features.
There are many other wallets that offer privacy [features], so you can look into some of that.