It seems like pure defense system. Why should anyone object to it?

Currently China's nuclear strike doctrine is "no first strike". To be clear, this means that China won't launch first, even in the case of a warning of a nuclear strike[1].

This isn't the same as the US or Russian policy (since 1993), which both retain the policy option of preemtive strikes.

Tools like THAAD reduce China's ability to present a credible second-strike, which has led them to object extremely strenuously to it.

Partially because of THAAD it seems that China is considering changing their doctrine[2]. This would be unfortunate, and it seems likely that there are many in the Chinese government who would prefer not to have to do that. If they could get THAAD deployment in Korea cancelled it would be likely to strengthen their hand.

[1] https://en.wikipedia.org/wiki/No_first_use

[2] http://thediplomat.com/2016/02/is-china-considering-a-high-r...

Because it breaks the doctrine of mutually assured destruction. If China loses the ability to effectively retaliate against a hypothetical US nuclear strike, it loses its superpower status.

THAAD isn't overly destablising to MAD, which operates on the strategic level. It has little effectiveness against ICBM re-entry vehicles which move very, very fast ( about 8 to 10 km / s ) and have all sorts of decoys and countermeasures.

It is designed for dealing with theatre missiles, IRBMs and the like, which move much more slowly, aren't well protected and aren't generally considered in the MAD calcul

Per state.gov:

Many of our regional defense deployments, like the Patriot system and the Terminal High Altitude Area Defense, or THAAD system, are inherently designed for theater use. They are not capable of defending against ICBMs launched at the United States. THAAD, however, is capable of defending against the medium-range and intermediate-range ballistic missile that North Korea is deploying.

China and NK consider themselves allies, as do the US and SK. And China+NK are not allied with US+SK. And that region is unlikely to be affected by any significant non-aligned players.

[It's a bit more complicated than that, of course. And THAAD isn't 100% effective. But the details don't change the overall picture much.]

If a missile is ever stopped by THAAD, it means SK+US didn't want it to land. Which probably means China+NK launched it, and did want it to land. Meanwhile, if SK+US decide to go on the offensive, THAAD won't stop their attack, but will mitigate any retaliation from China+NK.

THAAD is bad for China+NK in both scenarios.

In addition, since THAAD's existence makes it a whole lot less risky for US+SK to go on the offensive -- it makes it more likely that they would do so. And China+NK certainly wouldn't want to defend against a US+SK with THAAD being in place.

Because ABM was and is considered by most nations a threat to world peace as it increases the chance of a first strike by the party who has it. There was an Anti-ABM treaty which he US signed and then unilaterally withdrew from. US missile defense is progressing to the point of making the Russian (and Chinese) strategic arensals ineffective once it reaches that point the US can execute a first strike without fearing retaliation. Russia can't afford ABM so they are building new delivery systems, China doesn't have the tech nor does it seem to want to develop its nuclear arsenal any further. Both of them look at the US missile shield as a clear threat to their national security and regional and world peace because it would give the US the ability to do what every they want with impunity.

If one party in a standoff think they have a chance to survive/win they may turn aggressive.

Because the difference between a defensive system and and offensive system is only a few small modifications.