I noticed in Apple Mail, that the choice of font I had selected as the default for composing a new message did not have an italic face, and that caused the italic toolbar indicator to be inactive. When I pressed cmd+T (Font panel) and selected a different font that did have an italic face, then I was able to italicize the text in the compose window, either directly or by the toolbar italics control.

In my Mail settings, I have Lucida Grande 14 set for the message font and it has only Regular and Bold faces available.
Similarly, in Pages, your font choice would require an italic font face in order to set that character style. When it does, you select the text to be italicized and press cmd+i. Unlike MS Word, Pages does not create faux font results when the font is not installed.
Once you have achieved that, the same text from Pages can be copy/pasted into Mail and the italicized text remains in the compose window. The same keyboard shortcut (cmd+i) can be used to italicize selected Mail compose text when using a font supporting italic style.
Pages v13.1:
