@JPCarlos I am a Biblical scholar, and I can tell you that Psalm 139 is about God’s omniscience. If one continues reading verses 15 and 16, one sees that the poet goes on to say: “My frame was not hidden from you when I was made in the secret place, when I was woven together in the depths of the earth, Your eyes saw my unformed body; all the days ordained for me were written in your book before one of them came to be.” The passage from Isaiah is generally taken to be a reference to the Book of Psalms (as is Jeremiah 1:5, which similarly tells of God’s omniscience by reference to His knowledge of us before conception).
It is also worth mentioning that the talk of being woven together in the depths of the earth is directly parallel to a belief found in the ancient Greek mystery religions, which were historically quite influential on Judaism. According to these religions, human bodies were of chthonic (aka subterranean) origin and magically transported to the womb (which people back then believed was only a fertile resting place and not somewhere that a body could develop, thus why the various homuncular theories of human development originated at the same time).
This is just one of the many elements Judaism (and later, Christianity) borrowed from the Greek religions (especially pre-Olympian Greek religions). The doctrine is related to the ancient Greek view that we exist before conception even happens in the form of our soul, and that we must wait for our body to be fully formed so that we can then be attached to it. Many modern Christians prefer to interpret this borrowing as being purely metaphorical rather than a borrowing of literal belief, but of course that means that one can no longer rely on a literal reading of the passage to support any particular view about when life begins.
Furthermore, there is far more evidence that the Bible says life begins when one first draws birth. First, the words most commonly used to refer to the human soul or spirit, are נשמה (neshama = “breath”) and רוח (ruach = “wind,” or “breath” by analogy). For reference, the term “holy spirit” comes from רוח הקודש (ruach hakodesh). This equivalence of “soul” and “breath” can be found in many passages, such as Genesis 2:7, Genesis 7:15, Deuteronomy 20:16, Ecclesiastes 12:7, Isaiah 42:5, Job 33:4, Ezekiel 37:5–6, Joshua 11:11, 1 Kings 15:29, John 3:5–8, and John 20:22.
Again, there is a parallel to the Greek usage of πνευμα (pneuma = “wind” or “breath,” with a connotation of being in motion as in blowing). The other Greek word that means “soul,” ψυχη (psuche or psyche), also comes from the verb “to blow” (and eventually comes to mean “mind,” which is where we get “psyche” and “psychology”). Indeed, we see this and the previously mentioned chthonic elements of early Greek thought come together in Genesis 2:7 when God makes Adam’s body out of earth and then makes him into a living thing by breathing into him.
Finally, there are several passages in the Bible that suggest a fetus is not of any intrinsic value, some of which have already been referenced in previous answers. Exodus 21:22 tells us that the penalty for causing a miscarriage is a fine, whereas Exodus 21:23 tells us that the penalty for ending a life is to be killed oneself. It therefore follows that miscarriage must not, according to the law given in Exodus, count as ending a life. This is in keeping with Genesis 38:24, in which being pregnant does not prevent Tamar from being sentenced to immediate death by immolation. It also accords with Leviticus 27:1–7, in which we find out the monetary value of people by age and sex. No one below one month of age is given any value at all (just as how, in Numbers 3:15, only males a month old or more are considered persons to be counted by the census).
The clearest case, however, might be found in Numbers 5:11–31. There we learn that any man who has the merest suspicion that his wife might have been unfaithful may be brought to a priest for a test. If she is guilty, this test will abort whatever pregnancy might be in progress and sterilize her for life. If she is innocent, then she will not be harmed. Note that there is no consideration whatsoever to the possible fetus. All that matters in this scenario is that no man be forced to raise a child that he did not sire. Like the case of Tamar, pregnancy is not considered an extenuating circumstance.