In this case, the particular emotional appeal seems either insincere or unreasonable. Are people who have bad or deceased fathers offended by the very notion of Father's Day and the marketing around it? I doubt it, but even if they are, I think it would be entirely unreasonable, and rare enough for Google to risk or ignore.
Remember, anyone can choose at any time to be offended by anything, whether or not other people would consider them reasonable. People can also feign being offended to attempt to bring attention and credibility to an otherwise legitimate argument. Anyone who publishes any text on the Internet is liable to have someone claim the text to be offensive. I don't think any reasonable person would see this reminder and think that Google was mockingly telling them to call their abusive or dead father.
The reason it's important to talk about the emotions is that the emotional calculations change when the space or message is a personal one as opposed to a public one. It's the difference between someone coming up to you on the bus and asking you if you've called your father and a poster on the side of the bus asking if you've called your father. When you put your message in someone's personal space, you don't get to just say "eh, it's probably only a small fraction" because you're specifically communicating with specific people.
It is important to understand the emotional components of software.
> Are people who have bad or deceased fathers offended
> by the very notion of Father's Day and the marketing
> around it?
In the same way, the general idea of Father's Day is different than talking specifically to someone about their father. At that point, it is no longer impersonal (or easily dismissed as, "They are just talking to other people / people with happy father memories").
> It's pretty clear that Google doesn't know your father
> or your family situation, so their little reminder is
> a lot different that Bob Barker actually showing up at
> your house.
> Also, I don't get this assumption that your GMail is your
> own personal space.
* You may not 'own' it, but that doesn't mean there isn't an expectation of it being a semi-private space. You are leasing the use of your Gmail page from Google at the price of the ads being there. What if your landlord went door-to-door in your apartment complex telling everyone, "Call your father!" When your landlord shows up at your door, you don't know that he's going around to everyone. How would you not see that as personal?
* "Call your father" is a command, which is a lot more personal than "Father's day is coming up, you might want to call your father for free using our service!"
> There are ads on every single page
Do you not own your (purchased or gifted) copy of (e.g.) a newspaper? There are ads on every page.
> Google has a long history of sending out blanketed messages
> (e.g. new Labs features).
Your newspaper analogy is the most inconsistent yet. Of course you own your copy of a newspaper, and of course there are ads. But a newspaper is not your "personal space," and in fact, I'm sure most newspapers had Father's Day ads.