How can a commercial airliner which is made mostly comprised of empty space and lightweight aluminium penetrate a reinforced steel building?

The plane was heavy and loaded with fuel.  I went through Windows and not metal.  Please do not read on conspiracy sites.

Let me paraphrase your question; I'm too dumb to understand anything, therefore I must be right.

The more you talk the better it gets.   F = dp/dt.  Flight 175 was 150 tons @ 590 mph.  Flight 11 was 150 tons @ 465 mph.    You can play around with  diesel locomotive 212 tons at 100 mph and make your points about force dispersal. 

“How can a commercial airliner which is made mostly comprised of empty space and lightweight aluminium penetrate a reinforced steel building?”

The building is not reinforced steel.  It’s mainly glass and relatively thin concrete slabs to minimise construction costs.

________________

"like a hot knife through butter"?

Beware of overdramatic descriptions by journalists and others.

________________

“Shouldn't the majority of the plane's fuselage have crumpled upon impact and fell onto the ground? How could lightweight aluminum penetrate the tower and come out the other side?”

Not lightweight or weak.  Any idea how heavy a plane is?  The tubular shape gives immense strength in the axial direction (elementary engineering physics).

________________

“Is it like Force = Mass x Acceleration? If you have a bullet and throw it at someone, it has a small mass and small acceleration thus small force. Yet if the very same bullet was ejected from a gun it still has the same small mass but a huge amount of acceleration enabling it to penetrate someone body and seriously injure/kill them.”

No.  A dart rapidly accelerated will be equally penetrating as a dart of the same speed which has taken longer to speed up (smaller acceleration). It's impact speed, not acceleration, that counts.

________________

“So perhaps an aluminium plane with a small amount of acceleration doesn't have enough force to penetrate a building but if it's travelling at 580mph it can do some serious damage. Right?”

Totally wrong.  See previous question/answer.

_________________

I really wish people would make the effort to learn/understand basic science before misusing it to make incorrect claims.  It’s a bit like someone claiming election results were falsified simply because they wanted it to be true, but with zero actual evidence.

force F = mass m times speed change over time change 

speed change over time change (dV/dt) being the acceleration 

what changes with the sort of material is the deformation time dt , nevertheless the resulting force is extremely huge 

Momentum is conserved so no matter what material the plane is made of the FORCE of the building on the plane must bring all of the mass to a halt.  If travelling at 300 m/s and penetrating 30 m into the building this is 1/10 sec.  You have 2*10^5 kg of plane so the force = 2*10^5 *300 / (1/10)  = 6 * 10^8 N or about the equivalent of 60 million kg weight.  ( 60 thousand tonne ) It is the same idea as hitting a nail with a hammer.  The sudden stopping of the moving hammer creates high forces on the nail.  Even if the plane was made of butter or chalk the same forces would be present.  The only difference between this and a hardened steel projectile is that the plane crumples giving increased distance in which to slow the plane.  More distance -> more time-> lower force.  So if the plane was another 30m long the forces would HALVE to ONLY 30 million kg weight equivalent.

energy is mass times speed squared?

if it had done like a knife though (room-temperature) butter, it would have cut through the tower and flown out the other side

What "reinforced steel"??

The towers had a steel-frame core in the central "spine" area of the buildings.

The exterior was just glass and lightweight trim, having little strength.

[And before you start on the other idiot conspiracy claim:

Steel does not have to "melt" for a steel-frame building to collapse - it loses most of its strength by the time it reaches 600 degrees, and a timber fire is sufficient to collapse unprotected structural steel.

Steel frame building are totally reliant on fire-retardant coatings over the structural metalwork, to slow the heating from a fire, to give the occupants time to escape. Those coatings were never designed to stay in place when blasted with aircraft fragments, so the steelwork lost much of its protection, allowing it to be softened and trigger a collapse]. 

The Boeing 767 has a takeoff weight of 450,000 pounds. The aircraft were flying at max speeds when they hit~550 mph.

They had potential energies of ~ 660,000 HP.

The buildings were designed to withstand winds, Not aircraft. The majority of the damage was from fire of 30,000 gal of fuel burning.

You have answered the question.  It was the speed, and the glass windows of the skyscrapers, that accounted for the penetration.  Aircraft fuel is especially combustible and explosive.