All-vegetarian school still exploits and hurts animals by consuming other animal products

I found an article about an all-vegetarian School.
Quote from another article about the school:
"Students start out their day with bagels and cream cheese, whole-grain banana bread, egg and cheese roll-ups, to name a few of the offerings from this month."

I want to be positive and I like to encourage people when they are making choices towards veganism. However, I can't see how this is a step in the right direction. [Addition: well it may be if students choose to consume less animal products overall.] We have no data showing that this causes them to consume a lesser amount of animal products. [Add: But it seems it may be, see comment below.] I have even read of a school that does Meatless mondays, where it now is impossible to get a vegan meal at all during mondays, which was possible before they started with Meatless mondays. A vegan student was very sad about this; and of course it is a tragedy for the animals including all other people at that school also.

PETA making a public statement and celebrating this school, once again reinforces the idea that animal flesh is morally distinguishable from other animal foods.
I agree with the points made in this article: http://www.abolitionistapproach.com/vegan-mondays/
I think that if we want to encourage people to transition to veganism who say they can't become vegan at once, that we shouldn't encourage them to go lacto-ovo-"vegetarian" first, but to start with some vegan meals and then increase their amount of vegan meals (after we have stated how easy it is to go vegan at once, and that it is the only morally right thing to do). More of my ideas and suggestions: http://bloganders.blogspot.no/2013/04/the-way-to-transition-to-veganism-is.html

Finally,I would like to share these thoughts that I found today regarding terminology usage - if it is okay to use the term "vegetarian":

"Not in my view. The problem is at two levels.

First, the word "vegetarian" is now associated as a matter of word meaning with the consumption of animal products, whether dairy, eggs, or, in some cases, fish. There are "lacto-ovo-pesco-vegetarians." So using "vegetarian" perpetuates and reinforces this usage and meaning.
Second, vegans do not consume any animal products but they also do not wear or use animal products. "Vegetarianism," however it's interpreted, deals only with food. "Vegan" represents a a rejection of animal use.

If we mean "vegan," we should say "vegan," and not use "vegetarian," "veg," "veggie," veg*n," etc. There's enough confusion. Let's be clear."
https://www.facebook.com/abolitionistapproach

Thanks for reading! Have a wonderful day! :)


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Additional comments:
Grace Lorraine,
Thanks for your comment!
It seems this school serves much lesser animal products compared to other schools [note 1]. We can all help to inspire the leadership of that school to go all vegan in their menu.:
I think that if we share this story though, that we should be clear to tell our friends that their is no distinction between meat and other animal products in how it uses and exploits animals, and that veganism is the moral baseline.
1.
http://www.nydailynews.com/new-york/kids-enlighten-junk-food-loving-reporter-article-1.1331727