Why couldn't Adam and Eve keep both commandments? I hope this question is unique here, but I assure you I have searched and have not yet seen it. (This question is close, but not quite the same.)

Adam and Eve were given two commandments: 1) Multiply and replenish the earth, and 2) not eat of the forbidden fruit. From what I understand, some Christian denominations believe the commandments to be paradoxical; one cannot be kept without breaking the other.

Within the scope of those Christian denominations which view the two commandments as both impossible to keep while in the Garden of Eden: Why couldn't they keep both of these commandments, for surely they would have if they could?
...some Christian denominations believe the commandments to be paradoxical; one cannot be kept without breaking the other.

The short answer
There is no Biblical support for this.

The long answer
If some Christian denominations believe this, is it extra-biblical, e.g. Mormons, and so explanation will likely vary widely. (Actually, AFAIK, Mormonism is the only denomination that believes this.)
Perhaps you consider this the justification:

Why couldn't they keep both of these commandments, for surely they would have if they could?

But that is not necessarily true. Man was not infallable, and remember: the devil played a hand here too. It's not really temptation unless you can make the wrong choice.

FYI, Greg Bala said:

This question basically boils down to these types of questions:

Why did (how could) God create a creature that could choose poorly?

Did God know what we will fail?

Why didn't God create us without what is necessary to choose well?



While I do not believe these questions are what you are asking, these are the more commonly asked paradoxes/concerns about Adam and Eve.