Because it would need to be for us to be able to get a larger number by adding one.
All I'm saying is that infinity plus one is not larger than infinity. 1+1+1...infinity has the same value for instance as:
9*10^1 + 9*10^2 + 9*10^3....9*10^infinity. (an infinitely long string of 9's) Its all the same infinity.
So when I do
9*10^-1 + 9*10^-2 +9*10^-3...9*10^-infinity (an infinitely long string of 9's with a decimal point at the beginning) its equally poorly defined.
In the video, she points out that there is not number which is immediately less than any real number, because any number you choose which is less than c, must have infinite numbers between it and c due to the nature of the reals. Therefore, because .999... is a chosen number, it must be equal to c, or there must be a number between 0.999... and 1, which there clearly isn't. But what I argued above is that for any interval which is defined as containing all numbers less c, we can produce a .999... -like number which is clearly within the interval but by the same arguments must be equal to c, creating a contradiction. (and if you don't see a problem with that, let me tell you about my friend Charlie... he is TALL. So tall, we took him to a party with a lot of people, and everybody there was shorter than Charlie. Including Charlie himself! Now that's tall. 
)
But the real problem I see is that there is this curse of Babel with mathematics. For laughs, check out this, topic #4:
http://www.cracked.com/blog/6-innocent-sounding-topics-that-are-guaranteed-flame-wars/
Why is that? Its because we don't agree on what things mean. A lot of these things less defined than we like. My two cents is that we should admit human limitations, we should admit that at the end of the day, any number is going to be approximated to a human readable form. In that context, whatever calculations you do with with .999... are going to yield a result exactly the same as if you used 1, after being rounded down. rounding .999... to any degree of finite precision will give you 1. However, using the floor function instead of round will give you what I'm talking about: The largest number that is less than 1 within any arbitrary degree of precision you wish. That's useful too.
Curse of babel dispelled.
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