If using a mixer, then you should ideally be sending all coins to a brand new wallet, as opposed to back to a new address from the same wallet. There is always a chance that at some point in the future you mess up and accidentally link that new address to an old one or a change address from the same wallet, especially after months or years where you could easily forget which UTXOs were mixed and which weren't. There's also the possibility that someone gains access to your master public key, and then can derive all your address from that wallet and see that they are linked together.

It's not just about people sharing their private data willingly (which far too many people do), but it is also about your browsing habits. Some browsers, notable Chrome, monitor everything you do online. Many ISPs and governments also monitor their users and every webpage you visit. If you repeatedly visit the same address on a block explorer, it becomes pretty obvious to anyone watching you that you own that address, even if your wallet is offline/airgapped/paper/etc.

There are other possible leaks. For example, if you ever bought bitcoin from an exchange using Fiat you made KYC. If you send those coins from the exchange to your wallet it could even possible to link that to your bitcointalk account using a simple tool like that, if you are not careful.

This post was just to show people how easy it is to link all your addresses from the same wallet together.

I think this goes without saying. Even the newest newbie should realize that if they are handing over their KYC documents to an exchange, then all their activity can be linked to their real name. Perhaps what they don't realize is that many exchanges track where coins come from and go to before and after being on the exchange. They will ban users who deposit from/to casinos and even mixers. Since exchanges report user activity to their relevant governments, I wouldn't be surprised at all if they are also reporting which addresses are linked to which user, allowing the government to then trace your activity as well.

I don't really use exchanges, but I thought most would let you generate a new deposit address for each transaction, if you wanted? Do they really just give you one deposit address and that's it? What another great reason to stop using these exchanges. In this case, you will need to pass all your coins through a mixer prior to depositing them, and then again through a mixer after withdrawing them, but there are cases of some exchanges blocking transfers to/from mixers as I said above.

I think CryptoBridge exchange is still offering that option to generate new address every 15 minutes.

Would be nice if we can have a list of exchanges that have this option of generating new addresses.

We can conclude that privacy is a very challenging task today, and that most internet users including ones that use cryptocurrency do not have the knowledge and skills to remain anonymous. Even if we try to use VPN, Tor, mixers, coin control or any other way to ensure privacy, three-letter agencies are very likely a step or two ahead of us.

Snowden shows that NSA is working on tracking Bitcoin users at least from 2013 by using different spy tools (Xkeyscore. MAC addresses. OAKSTAR. MONKEYROCKET), and it is not difficult to imagine what they have accomplished to this day.

At Bitcoin conference Snowden is say : “The lack of privacy is an existential threat to bitcoin. Is the only protection users have from political change,”, but also: “If you know how the system works, you can still have privacy,”

Wallet addresses are not generated automatically upon joining, most of the time the users need to click a "generate address" button.
Kraken is the only exchange I've been using that lets you generate a new address, I've never see another one.
If most exchanges don't provide it, I suppose it's a matter of infrastructure convenience (or security)

it has always been.

It's not about security, it's just that generating new addresses requires some extra coding and maybe extra work for support when people send coins to old addresses, so they don't see reasons to do it, because so far it worked well for them - users almost never complain about it, because they don't care about their privacy. I think it just shows that an average exchange users doesn't care much about Bitcoin's ideals, they just want to make money (and that's okay).

Walletexplorers won't help other people identify your personal identity but it will only help you connect all the addresses being used in one wallet, that is why this has been a big tool for alt account hunters linking bounty abusers in the forum. It may link members here and their alt accounts but it can't show you anything about the identity of the owner of that wallet. As long as you don't use your address publicly or is not tied up to you in anyway on any KYC process then the addresses you are using will remain anonymous and can't be linked to you.

As far as I am concerned, if you care about your privacy, then avoid KYC demanding exchanges altogether.

If you complete KYC, you have no idea how many people at that exchange have access to the information linking your real name to your deposit and withdrawal addresses. You also have no idea which third parties or governments the exchange is either selling or passing on your details to, and how many people at each of those have access to this information. If you mix coins before depositing or after withdrawing, some exchanges may freeze your account due to unspecified "suspicious activity" until you complete even more invasive KYC.

With the ongoing growth of exchanges like LocalBitcoin, Paxful, and BISQ, as well as a large peer-to-peer marketplace on this forum and others, there isn't really an absolute need to use a centralized exchange. Sure, it might be easier and quicker, but it's very rare that using one is your only option.