> I can’t see a reason why this is all not equal on both sides.

I can.

Think of what employment is for a second: shareholders (or company owners) own the capital, and the employee gets to follow orders. Structurally, the company pay workers less than their actual value: shareholders gotta hold, and they squeeze the margin out of the employee. The margin may be thin, but it's never meant to be zero (except for non-profits, but they're the exception).

Such a relationship is fundamentally asymmetrical, such an exchange fundamentally unequal. If you want any hope of restoring fairness from this system, termination conditions have to be asymmetrical as well.

And I can’t see a reason why it should be equal. Even if you strip the relationship down to its most basic principle, there is asymmetry. One party provides work with the expectation of pay, the other party providess pay with the expectation of work.

But the asymmetries don’t end there. Terminating employment is a far greater threat to the employee than the employer. This creates a power imbalance which could easily be exploited by malicious or incompetent employers. That power imbalance is fundamental to this relationship and is reason enough (in the opinion of many countries) to bolster worker rights.