Just to add to Rob's answer:
and then you are given a seed phrase with 12 random words
The words aren't completely random. They are selected from a list of 2048 words - which themselves have been specifically chosen to reduce the likelihood of confusing two or more of them. (e.g. When trying to remember them, or when salvaging a wallet because your dog ate two of them...)
Given that the context of your question is Metamask, the wordlist (it's the same for any tool that uses BIP-39... ) is used by Metamask by way of the
bip39 NPM package, the wordlist for which is here: https://github.com/bitcoin/bips/blob/master/bip-0039/english.txt
Is it possible to define your own 12-word seed phrase?
Or: Can I just pick 12 words from the wordlist and remove the need to trust a tool?
Not all combinations of 12 words from the list are valid†.
What you can do is choose 12 words from the list, then feed them into the tool that Rob pointed to. If it's not a valid combination a big orange warning message will appear.
† (There are 204812 combinations, but only 204811 * 2048/(11-4) are valid - some combinations are lost due to the need to checksum.)
With regards to different languages, you have the choice of the following wordlists:
However, you can't mix words from the different lists: all 12 words have to be in the same language.