The firstborn are depicted as being closer to the divine than men, and generally as a rule more beautiful and powerful, but the sticking point in this argument about their "angelic" nature is their capacity for evil. They are capable of greater goodness but also deeper evil because of their high and mighty nature. The Noldor of the House of Feanor are guilty of possibly the greatest sins of any being that is not in the service of the Enemy (the Kinslaying, and all the horror that followed), except arguably that of the last king of Numenor (war on Aman).
What he may be getting at is that usually the elves are shown to be unwavering foes of Morgoth and Sauron, and they have special powers that make them more similar to and closer to the valar and maiar, and also kinship with the elves is consistently used as a sign that a mortal character or a tribe of men/dwarves are more trustworthy and wise ("elf-friends" are pretty much always good guys). Not exactly angels per se (that would be the maiar), but "angelic"? Sort of yes.