The reason that an embryo shouldn't be protected is the same reason that the "life" of a tissue biopsy shouldn't be protected: despite being alive, it doesn't yet any of the key qualities that we recognize in each other as compassionate sentient beings.

Of course, eventually, the developmental process proceeds enough so that we do have those key qualities, and then that life should be protected. And there's the messy in-between phase where the attributes are gradually acquired.

But just like with the classical philosophical conundrum about a pile of sand--how many grains do you need to have a pile?--our discomfiture at not having a crisp trivially-recognizable demarkation between states ("not a pile" vs "pile", or "not having personhood" vs "having personhood") does not mean we can declare to everyone: "two grains of sand is a pile because even though it's nonsense, it's clear".