Instructor can't talk when H10-13.4 is plugged in I'm a student pilot and I just bought my first own headset because the standard one in the plane does not really fit me.

I got a david clark h10-13.4. 
My instructor uses either his private Bose A20 or the standard (active) Aerostar that is in the plane.

Today I tried my DC-headset for the fist time and there was a problem: I could talk just fine and the mic worked great but I could not hear my instructor anymore. He had to yell into the microphone to activate the intercom and even when he was loud enough, the sound quality was aweful. This was the same for both the A20 and the Aerostar headset. 
Also others could not hear him when he tried to communicate with other aircraft over radio. They said there was just noise transmitted. 

As soon as I switched back to the Aerostar headset, everything was fine again.

After today's flights I tried to use my headset with a handheld radio and the quality of my transmission was good (both ways). 

My first idea is an impedance- or level-mismatch; but I thought, all fixed-wing  aviation headsets had about the same impedance. 
Are there ready-built circuits to adapt my headset to the intercom?

I really don't want to stick with the standard headset. Neither do I want to blow 1k€ on a Bose as I really like the H10.

Apart from it being a Becker I don't know anything about the radio in the plane but I've been told not to mess with the configuration of the radio, as it works in all other setups. 

Edit:
After having found a datasheet for both the A20 and the H10-13.4 I'm more confused than before. 

DC-Headset-Datasheet: http://www.davidclarkcompany.com/files/literature/10-13.4.pdf

A20-Datasheet: https://assets.bose.com/content/dam/Bose_DAM/Web/consumer_electronics/global/products/headphones/a20_aviation_headset_Orion/pdf/a20_hdst_PDF_ownersguide_EN.pdf

On page 38 of the A20's datasheet there is the technical data with the microphone output levels. It sais:


  Typical output is 600 mV at 114 dB SPL


The David Clark sais:


  Mic Sensitivity: 400mV+/-6dB into 150Ω load @ 1kHz for 114 dB SPL input


which seems to be tested under the same conditions. But the amplitude of the Bose is higher. Shouldn't the effect we have seen be the other way around? With his mic working and mine not activating the intercom? Or with him being very distorted due to clipping in the amplifier?
Hope someone knows better than me.
So after Juan's help and also talking to Becker I think I've found the answer: 

It's an unlucky impedance combination.

That means maybe I can get it to work by lowering the VOX-level (increase mic bias) far enough so my instructor can activate it but if I lower it too much, my own mic will constantly activate the intercom, resulting in constant noise.

Becker told me, this is likely due to an old wiring version being installed where both pilot and copilot's mic are connected in parallel to the same amplifier. So when my mic has a 'better efficiency' i.e. better conversion from mechanical swing to voltage, the VOX adapts the threshold (or as Becker said the bias voltage for the mic) for this and the amplitude of the co's mic is to low to activate it. 
A fix would at least require rewiring of the system to have dedicated amplifiers and bias supplies for both the pilot and co-pilot.

I think I confused some things in the physics here; if you point me to it, I will gladly correct it.

In general Becker's advise was to always use the same kind of headset for both pilot and all passengers in order to ensure best results (all volumes will be the same for all people then).