If someone is being hypocritical, that situation may be perceived as 'ironic' by a listener who is aware of the hypocrisy, but the hypocrite is not 'being ironical' in a rhetorical sense. In verbal irony a speaker knowingly says something meaning it to contrast, in the mind of the listener, with the literal meaning of what he or she says. In conscious hypocrisy a speaker says something that he or she intends to be understood as true or sincere, when he or she is aware that the true situation is at odds with this. In unconscious hypocrisy a speaker says something that he or she intends to be understood as true or sincere, but is not aware that the true situation is at odds with this.
Put briefly, both irony and hypocrisy pretend, the first to reveal, the second to conceal.
To answer your direct question, if you tell your friend that it is ironic that he or she said something, and they ask why, you are still faced with having to bring up, implicitly or explicitly, the notion of hypocrisy.
An interesting blog I found emphasises that irony involves the juxtaposition of opposites, and "ironic" should not be used to mean merely "interesting", "funny", etc, and gives a number of examples, including this example of how hypocrisy might, as a borderline case, be ironic:
"I find it ironic that you pointed out grammar mistakes in my post but
you ended up making grammar mistakes yourself as well."
Also a border case. Technically speaking there are no opposites being
juxtaposed here. Person A lectures person B about grammar, and makes
grammatical mistakes himself as well. No opposites happening here, so
no irony. "Hypocrisy" might be a better word in this case.
On the other hand, some juxtaposition can be seen here in another
sense. If someone lectures someone else about grammar, one could
assume that he should know what he's talking about, but since he made
grammatical mistakes himself, it's clear that he is not as
knowledgeable as he pretends. Thus there's a juxtaposition between
what this person pretends to be and what he actually is. That could be
seen as ironic.
Abuse of irony/ironic