You have noticed a very peculiar aspect of English vocabulary. As rich as it is in comparison to many other languages, due to its almost creole history, it really is impoverished in comparison to other languages in kinship terms.
But 'why' is always a difficult question, especially when mixed with cultural questions. There are the difficulties with Sapir-Whorf type explanations: both language restricting thought on one hand and the number of Eskimo words for snow on the other.
Does the lack of kinship terms reflect the cultural lack of warmth and caring for relatives among English speakers, that is not caring leads to the loss of the words (which etymologically do exist in the ancestor languages), or did the arbitrary lack of kinship terms contribute to the crumbling of English family values?
Any direction sounds much too tendentious, too judgmental, and requires too much unjustified and biased assumptions to choose.
The comparative lack of kinship terms does ask for an explanation but one backed up by linguistic and anthropological and comparative research. The only source that comes to mind is Levi-Strauss's 'The Elementary Structures of Kinship.' (primarily anthropological but as a by product a number of examples of kinship term systems.
English isn't alone in having relatively few kinship terms. Some other European languages have only a few extra (French, German) and some languages really only have names for their clan and generation (anybody of one's biological parents' generation might be called something like 'uncle' or 'aunt', even one's birth parents).
Having no definite answer to your question, I can only say beware of making cultural inferences based on restrictions to languages. Some languages have grammatical gender and others don't, but that doesn't mean the ones without can't recognize the sex of other people.
I suspect they are, too - you'll be having co-son and co-son's mate next!
Seriously, you are talking about in-laws here.
From Wikipedia:
A brother-in-law (plural brothers-in-law) is the brother of one's spouse, the husband of one's sibling, the husband of one's spouse's sibling [relevant in the first case you mention], or the brother of one's sibling's spouse.
You can work out what sister-in-law covers.
Oh, and the perhaps unfamiliar terms used by Wikipedia:
sibling - a brother or sister
spouse - a husband or wife
... that is, they are hypernyms (like cutlery for knives, forks, ...)
Best Answer
He is your brother-in-law.
There has already been a similar question posted here to which the answer was "sister-in-law", so I'll finish the list here:
Your spouse's brother or your sister's husband is your brother-in-law.
Your spouse's sister or your brother's wife is your sister-in-law.
Your spouse's father is your father-in-law.
Your spouse's mother is your mother-in-law.
Your daughter's husband is your son-in-law.
Your son's wife is your daughter-in-law.
Where applicable (and where disowning has not occurred), you child's same-sex life partner under a legal bond (whether marriage or civil union or what have you) or a bond you recognise even when the law does not would be either a son-in-law or daughter-in-law, as applicable.