Because if it’s zero, they don’t learn anything when no one leaves. Take the example where there is 1 islander with blue eyes. Guru says “I see 0 islanders with blue eyes”. He doesn’t learn anything, and doesn’t leave. Now take the case of 2 islanders with blue eyes. Each sees the other, knows that the guru is lying, but doesn’t know that the blue eyed islander they can see knows that she’s lying. It is possible that they have brown eyes, and thus that the blue eyed islander they see sees no blue eyes and believes the guru. Even though they know the guru is lying, it doesn’t create the kind of common knowledge necessary to induce their own eye color.
The reason the guru can say any number greater than zero and it will work from that number is that, if there were only that number islanders with blue eyes, they would leave on the first day. If she said 10, 10 blue eyed islanders would leave the first day. 11 would learn when 10 didn’t leave that they too have blue eyes, and would leave on the second day. 12 would learn when 11 didn’t leave, etc.
It’s not just a matter of all agreeing on the same number and counting, but that the guru tells them something about the number: if there were only this many of you, they would leave on the first day, i.e. that they would know their eye color on the first day. That allows for the nested hypothetical of what the others know that the others know that the others know … to bottom out at the number the guru says. If it didn’t bottom out, it would get to zero and no one would leave. But it can bottom out at any number. If the guru says “I see 10 with blue eyes”, they know on day 1 what they wouldn’t learn until day 10 in the case where the guru says “I see 1 with blue eyes”: that there are at least 10 islanders with blue eyes.
The argument in which I defended the accepted understanding of special relativity against your attempt to disprove it? Of course the only explanation for why I refused to admit that I (and Einstein) were wrong about special relativity was that my fragile ego. What other explanation could there be…