Verbal preference upon meeting people or meeting with others

Question

Is it correct to think that these mean the following and when would the sentences below the descriptions of each one of the verbs that I have be preferred to say? Why would one use a reflexive form of the verb? :

ВСТРЕ́ТИЛ - more general notion that includes meeting people for the first time, meeting up your friends, and just seeing someone without even talking at all.

ПОЗНАКО́МИМСЯ - to meet someone for the first time and talk a bit at least, to find out the person’s name and some other things you might be interested in

Я ВСТРЕ́ТИЛ твоего́ брата в метро́.

Мы ВСТРЕ́ТИЛИСЬ с твои́м братом в метро́.

Мы ВСТРЕ́ТИЛИ твоего́ бо́сса в го́роде.

Мы ВСТРЕ́ТИЛИСЬ с твои́м бо́ссом в торго́вом це́нтре.

Answer 1

Literal meaning of встречать is to be on/by the way of someone/something, e.g. встречать врага во всеоружии. It relates to physical location of object. Reciprocal voice встретиться describes mutual process of physical relocation to the same location.

Literal meaning of знакомить is to give knowledge about subject and in reflexive form знакомиться is to obtain (give to him/her self) knowledge about subject.