In this episode of Bitcoin, Explained, hosts Aaron van Wirdum and Sjors Provoost discuss reusing Bitcoin addresses. More specifically, they explain why reusing Bitcoin addresses is a bad idea.

Reusing Bitcoin addresses is a bad idea for roughly three reasons. The first two of these are that it harms privacy and impedes on the censorship resistance of Bitcoin. In the episode, Aaron and Sjors go over a couple examples of how such a loss of privacy and censorship resistance can negatively affect Bitcoin users.

The third reason that reusing Bitcoin addresses is a bad idea, is that it opens up the possibility of some niche attacks. In certain cases, attackers could extract private keys from signatures after coins are first spent from an address — though this does require that a wallet implemented the signing algorithm wrongly in the first place. There are also some scenarios where quantum computers could in the future extract private keys from signatures if addresses are reused.

Another type of niche attack is a timing sidechannel attack, such as the recently disclosed Hertzbleed Attack. Sjors explains that attackers can potentially derive a private key from a wallet by closely monitoring how the computer that hosts the wallet behaves when signing a transaction. This attack is more plausible if addresses are reused.

Address reuse wiki: https://en.bitcoin.it/wiki/Address_reuse#Security
Hertzbleed attack: https://www.hertzbleed.com/