Two reasons: 1) they are a lot shorter for the same level of security and 2) any random number can be an Ed25519 key. To generate an RSA you have to generate two large random primes, and the code that does this is complicated an so can more easily be (and in the past has been) compromised to generate weak keys.

What I don't get then is how can a short key be secure, that goes against what I was taught in college. Aren't shorter keys more prone to collisions and bruteforce attacks?

Given the same cipher, more or less, yes. Between ciphers, though, key-lengths are less relevant, and the differences in those ciphers become more so.

EDIT: Think of it in terms of Shannon Entropy: because RSA requires a pair of primes, the keyspace is so much sparser — that is to say, more "predictable" (if, granted, at a mostly theoretical level) — so keys need to be that much larger to be secure.

Contrarily, with ED25519, keys can be smaller, because the keyspace is denser.

(Or am I just talking out my ass here?)

EDIT 2: s/smaller/sparser/, s/bigger/denser/, regarding keyspaces. Thanks, 'lisper!

The other factor (no pun intended) that makes RSA keys large is that there are more efficient algorithms for factoring than there are for solving the elliptic curve discrete log problem, e.g. https://en.wikipedia.org/wiki/General_number_field_sieve If you crunch the numbers on this you will find that a 2000-bit RSA key has a security level of about 100 bits, i.e. it takes about 2^100 operations to factor a 2000-bit RSA key using GNFS.

Exactly. Generating random primes is not terribly difficult in theory, but in practice it is very tricky, which makes it hard to answer the question: how do you know you can trust your keys? Sure, you can verify that your primes are prime, but how do you know how much entropy they have? The only way to figure that out is the audit the code. (And then you have the problem of making sure that the code you're running is the code you audited.)

Generating random numbers is also tricky, but a lot less so than generating random primes: take an entropy source and run it through a whitener, i.e. feed it to sha512. As long as you have a reliable estimate of the lower bound of the quality of your entropy source, you're good. A lot fewer moving parts.

OpenSSH already has support built in, as does Mosh, and therefore, I do think it's worth it.

I do sometimes disagree with using keys though, despite everyone pushing it so hard, there are cases where I think passwords are the way to go, but thats a long post for another time.

Also, I really like usin pam auth mods, such as yubikeys or google auth for two factor. That combined with regular hardening, and yes Ill admit it, non standard ports (reduces log alert fatique) does a pretty good job.

That sounds interesting, could you elaborate on that?

ECC and RSA are both ultimately going to fall to practical quantum computing, and probably over a time frame short enough that it won't matter which cipher you picked.