Example if GMail used Comet, your Inbox would get updated the second you got a new mail instead of every x minutes.
You can achieve something close to it by using very insistent polling but this causes an unreasonable load on the server. Whereas with push technology you can get live updates without this unnecessary load.
Your most compelling argument would be something like "GMail would be 10x as popular with sub-second client updates and Comet would make that possible with the existing resources."
Note that the premise is clearly false - GMail would not be significantly more popular with subsecond client updates. That leaves you arguing that push would save resources but I'd guess that the current polling intervals are such that 10% is spent on them, which limits the benefits to 10%.
You need to show that comet enables valuable new apps, makes existing apps significantly more valuable to users, or makes it easier to produce new apps. And, even if you do, you're not going to make much money.
Note the weasel word "most" - your best argument isn't all that good. Your users, the app writers, are going to make far more money.
Google chat couldn't exist without Comet, (unless they redid the entire thing in Flash and please don't get me started on the whole Flash/Silverlight mess)
A lot of tech decisions don't deliver 10x improvement in the value-add for you users, but even a 10% value-add can be a powerful differentiator in a competitive market.
And finally Comet isn't really a significant technological hurdle. Implementing it versus simple AJAX isn't a very big increase in your tech efforts and might be very much worthwhile.
I'm not saying you should use Coment in all your future web dev, this isn't fanboism. Just spend an hour or two to get a rudimentary understanding of the technology its costs & benefits so you can decide for yourself if it is a good fit for your next project.
There is no "comet vs. ajax" dichotomy. Comet employs ajax as a means to interpret data pushed from the server. If your application needs asynchronous, live updates, then you need Comet or Flash. If you use Comet, you'll undoubtedly be using Ajax as well.
You can achieve something close to it by using very insistent polling but this causes an unreasonable load on the server. Whereas with push technology you can get live updates without this unnecessary load.
How is that for a compelling argument?