No, it should not piss off any employer!
The equity that is offered to you to as part of your employment is remuneration for your efforts. The employer should not be upset at you for wanting to convert that to cash. It is true that the employer might not want their stock to go to outside parties. In that case, they should arrange for alternate arrangements (buybacks, employee-liquidity in funding rounds etc). But you are not doing anything inherently unethical to warrant any retaliation.
All reasons why managers might make life difficult for said employee after the fact.
With that said, it's obviously in their interest to provide some liquidity to avoid their long-time employees from defecting to GOOG or NFLX or FB, which reward with perfectly liquid stock grants, so in case of demand from the buy-side an employer would orchestrate a secondary market transaction. On the buy side in most cases you'd see an SPV managed by the VC who invested in previous rounds (which helps with keeping the cap table low).
Ironically, for smaller VCs entire economics of their firms are based on these SPVs (which sometimes charge upwards of 2% management fee on top of 20% carry - and that's for a chunk shares sitting quietly doing nothing).
Does this generally piss off the employer? I wonder if the employee faced any sort of retaliation or anything from this.