Why is it illegal to possess Cuban cigars or is it?

As I understand it, if a company does business with Cuba, they are not allowed to do business in USA. This does not affect many small, mid-size companies, but its a big issue for bigger ones (say Toyota, Merck, Roche, Sony, etc.) who can not afford to lose the US market over a few pesos in Cuba.

Let me pose this hypothetical:

I’m an American. Suppose as a graduation gift, someone gives me one Cuban cigar he recently bought in Canada. Not being a smoker, I just stash it away somewhere in my house. Have I broken the law and, if tipped off, does the government have as much cause to search my house and arrest me as it would if had several kilos of heroin?

Which raises the interesting question of "How many links in the chain are still considered “doing business with Cuba”? I mean, a liquor store stocking Havana Club rum didn’t buy it directly from Castro, after all. They likely purchased it from a wholesaler. Who probably got it from an importer. Are they all considered to be “doing business with Cuba”, or just the importer?

Havana Club rum made in Cuba cannot be legally sold by anyone in the US. Bacardi sells a rum in the US called Havana Club that is made in Puerto Rico.

I live in Australia. The Havana Club rum we have here is made in Cuba. It even has an official Seal of Guarantee on the bottle from the Cuban Government certifying that it really is Cuban rum. Seriously.

I believe you. I guess I didn’t understand your point. All the links in your chain are doing business with Cuba, which is entirely legal in Australia. Does that have anything to do with the US embargo?

Someone upthread said that any company doing business with Cuba couldn’t also do business in the US. I was trying to clarify where the dividing line was between “Doing business with Cuba” (eg actually importing their product) and simply being a retailer who happened to sell Cuban goods amongst many, many, many other non-Cuban goods.

For example, if I buy a bottle of Wild Turkey, I wouldn’t say that I’d been doing business with America to get it. I’ve been doing business with my local liquor retailer, who in turn has been doing business with a wholesaler, who has been doing business with an importer, who in turn has been doing business with America to get it; if that makes sense.

The Helms-Burton Act, which defines the embargo, estates in it’s Title III that sanctions “may also be applied to non-U.S. companies trading with Cuba.” This restriction also applies to maritime shipping, as ships docking at Cuban ports are not allowed to dock at U.S. ports for six months.
The trading with Cuba part refers to " purchase, transport, import, or otherwise
deal in or engage in any transaction
with respect to any merchandise
outside the United States if such merchandise:
(1) Is of Cuban origin; or
(2) Is or has been located in or transported
from or through Cuba; or
(3) Is made or derived in whole or in
part of any article which is the growth,
produce or manufacture of Cuba. "

As this is related to the goods themselves, it apepars that everyone in your chain of supply, as far as it’s a company (so this excludes you, the final purchaser), “may” have santions applied. These sanctions also include “deny entry to the U.S. of the leadership of such companies”.
Legal document in PDF.

All this said, the truth appears to be, as stated up thread, that Cuban cigars are illegal, and Chinese tea is not, just because there are a lot of cuban-american votes in Florida, while not enough chinese-american votes in California (or wherever). Most of those Cuban-american votes come from second generation immigrants from Cuba, whose parents were expropriated of their properties, and have no sympathy for a revolution that converted them form elite citizens in the island to ‘second class’ refugees in Florida.

Then once they realize how horrible things are you’d think they’d want to go back. They don’t.
I am certain many Cubans are quite happy there, but they aren’t the sort to go through all that trouble to leave.