the starting and idle system is working fine .. These require small amounts of fuel and air.
But when you open the throttle to take off, the carb senses this and another internal system takes over.. and this one has problems.
Normally, opening the throttle would provided a balance of an increased amount or air and fuel.
The throttle plate or slide does open making more air available, but for some reason there seems to be no additional fuel available.. so the engine dies.
A common caused is a tiny piece of dirt blocking some orifice or fuel-jet inside the carb.. and a carb cleaning will clear it up.