The UK did not invoke article 5 of nato that would have compelled other members to get involved. The only time article 5 was invoked was september 11/afghanistan related. NATO also only requires action is the attack occours in Europe or north america/north atlantic. As the attack was in the south atlantic they technically couldn't invoke article 5 even if they wanted to.

So no country was obliged to help, but why didn't any offer to help?

Well Australian and New zealand sorta did. Their navies offered to cover various patrol duties in the pacific and indian oceans that freed up Royal navy vessels for use in the atlantic.

The US was also in a bind that it was allied to both countries, but its alliance to argentina was also defensively only, as argentina was the aggressor, and they didn't try and invoke the alliance so the US weren't obliged to help.

However they sorta helped anyway. They imposed sanctions on Argentina, offered access to US air fields for supply flights and reportedly offered use of a carrier group in May but the conflict was over before they could have realistically gotten involved.