Confusion about manquer example

In this specific context and usage of manquer, rater (can be - to miss/to fail) is an alternative - that is for missing (not catching) transport or failing to attend an event etc  In familiar use 'rater' is definitely heard in this context. By extension, this snippet informs that 'rater' is not synonymous with manquer when it means to lack something or miss something 'emotionally'.

Just to give an example:

My brother moved out. I miss him. -- Mon frère a démenagé. Il me manque.
My brother was late, I missed him. -- Mon frère avait du retard, je l'ai raté.

I understand how it is used but wonder why it is used in manquer lesson since I don’t see the word mentioned in the lesson. It doesn’t matter. Thank you.

There is a brief mention in the lesson to explain, and then an example - easy to 'miss' perhaps:

In French, you can also use the verb rater in this specific context, though it's a bit more familiar than manquer.