...why Chopin's two concerti are mixed up? Why was his second one published first and vice verse?

It was a question of the date of publication.

The Henle edition of the concertos explains it as follows :

"The Concerto in e minor for piano and orchestra was composed in 1830 after Chopin had completed his f-minor Concerto. Nonetheless, it was the first of the two to be published, appearing in 1833 as op. 11 whereas the f-minor Concerto did not reach print until 1836, when it appeared as op. 21."

Why Chopin didn't get the Concertos to the publisher in the order in which he composed them is another question.

Regards,

It all gets somewhat confusing, if we assume that the opus number is the order the music was composed, or at least, completed. Beethoven's first two piano concertos suffer from a similar affliction: the C major is actually the second to be composed. And even worse, his Op.49 sonatas are juvenilia, composed prior to his Op.2, and Beethoven never meant them to be published.

Peter Gould [1] makes brief reference, with no explanation, as follows :

" ... the two concertos, written successively just before his twentieth birthday. [...] The F minor Concerto, O. 21, described as 'number two', was actually written first. [...] The e minor Concerto, called 'number one' because of the delay in publishing the F minor ..."

[1] Peter Gould. "Sonatas and Concertos" in Frederic Chopin; Profiles of the Man and the Musician. (pp. 144-69) ed. Alan Walker. Barrie and Rockliff, London, 1966.

Regards,