2 Hg Team damage vs player damage
Dealing 10 damage to a single player will not kill a team that has 20 life. This is where you are going wrong:


  the single player life is the (total life)/2


This might have been true years ago (more on that later), but by current rules, individual players in two-headed giant do not have life totals. You cannot divide the total life in half and assign that to each player. The shared life total is the only life total that a team has.


Correct: The team has 30 life. 
Incorrect: Each individual player has 30 &div; 2 life.


On the other hand, if the opposing team had 20 life, and you somehow dealt 10 damage to each opponent (e.g., with Fall of the Titans), then you would kill the opposing team.

Another user discovered that, prior to April 23, 2010, a rule for life totals in two-headed giant stated:


  If an effect needs to know the value of an individual player's life total, that effect uses the team's life total divided by two, rounded up, instead.


With the release of Rise of the Eldrazi, the rule changed:


  If a cost or effect needs to know the value of an individual player's life total, that cost or effect uses the team's life total instead.


This could explain part of your confusion. I omitted rule numbers intentionally, because they don't line up exactly with the current rules.