Table Stakes in All-In Poker

Dear Mark,
The answer to this question is probably right in front of my eyes, but I cannot see it. I was watching a Poker tournament on the Travel channel when player A, after seeing his first two cards, bets $10,000. Player B, still in the game but with far fewer chips, pushes all his chips to the center and states "all-in."
My question is, why can player B, with far fewer chips and unable to sustain the future raises of player A, still be able to challenge Player A? Ralph I.
Key to this mystery is the "All-in." Poker in most casinos is played as "table stakes," meaning that only the chips in play at the beginning of each the hand can be used throughout that hand.
The table stakes rule has a handmaiden rule, called the "All-In": a player cannot be forced to forfeit a hand simply because he/she lacks sufficient chips to call the bet. A player who does not have enough chips to call a bet is declared All-In.
That player, if a winner, qualifies for only that portion of the pot as it stood at the time of his final wager, not the whole pot. All further action among the other players, following a bettor's "All-in" declaration, takes place in a "side pot," which is inaccessible to the All-In player.