Objection 1. It would seem that pride was not the first man's first sin. For the Apostle says (Romans 5:19) that "by the disobedience of one man many were made sinners." Now the first man's first sin is the one by which all men were made sinners in the point of original sin. Therefore disobedience, and not pride, was the first man's first sin.
Objection 2. Further, Ambrose says, commenting on Luke 4:3, "And the devil said to Him," that the devil in tempting Christ observed the same order as in overcoming the first man. Now Christ was first tempted to gluttony, as appears from Matthew 4:3, where it was said to Him: "If thou be the Son of God, command that these stones be made bread." Therefore the first man's first sin was not pride but gluttony.
Objection 3. Further, man sinned at the devil's suggestion. Now the devil in tempting man promised him knowledge (Genesis 3:5). Therefore inordinateness in man was through the desire of knowledge, which pertains to curiosity. Therefore curiosity, and not pride, was the first sin.
Objection 4. Further, a gloss [St. Augustine, Gen. ad lit. xi] on 1 Timothy 2:14, "The woman being seduced was in the transgression," says: "The Apostle rightly calls this seduction, for they were persuaded to accept a falsehood as being true; namely that God had forbidden them to touch that tree, because He knew that if they touched it, they would be like gods, as though He who made them men, begrudged them the godhead..." Now it pertains to unbelief to believe such a thing. Therefore man's first sin was unbelief and not pride.
On the contrary, It is written (Sirach 10:15): "Pride is the beginning of all sin." Now man's first sin is the beginning of all sin, according to Romans 5:12, "By one man sin entered into this world." Therefore man's first sin was pride.
I answer that, Many movements may concur towards one sin, and the character of sin attaches to that one in which inordinateness is first found. And it is evident that inordinateness is in the inward movement of the soul before being in the outward act of the body; since, as Augustine says (De Civ. Dei i, 18), the sanctity of the body is not forfeited so long as the sanctity of the soul remains. Also, among the inward movements, the appetite is moved towards the end before being moved towards that which is desired for the sake of the end; and consequently man's first sin was where it was possible for his appetite to be directed to an inordinate end. Now man was so appointed in the state of innocence, that there was no rebellion of the flesh against the spirit. Wherefore it was not possible for the first inordinateness in the human appetite to result from his coveting a sensible good, to which the concupiscence of the flesh tends against the order of reason. It remains therefore that the first inordinateness of the human appetite resulted from his coveting inordinately some spiritual good. Now he would not have coveted it inordinately, by desiring it according to his measure as established by the Divine rule. Hence it follows that man's first sin consisted in his coveting some spiritual good above his measure: and this pertains to pride. Therefore it is evident that man's first sin was pride.
Reply to Objection 1. Man's disobedience to the Divine command was not willed by man for his own sake, for this could not happen unless one presuppose inordinateness in his will. It remains therefore that he willed it for the sake of something else. Now the first thing he coveted inordinately was his own excellence; and consequently his disobedience was the result of his pride. This agrees with the statement of Augustine, who says (Ad Oros [Dial. QQ. lxv, qu. 4) that "man puffed up with pride obeyed the serpent's prompting, and scorned God's commands."
Reply to Objection 2. Gluttony also had a place in the sin of our first parents. For it is written (Genesis 3:6): "The woman saw that the tree was good to eat, and fair to the eyes, and delightful to behold, and she took of the fruit thereof, and did eat." Yet the very goodness and beauty of the fruit was not their first motive for sinning, but the persuasive words of the serpent, who said (Genesis 3:5): "Your eyes shall be opened and you shall be as Gods": and it was by coveting this that the woman fell into pride. Hence the sin of gluttony resulted from the sin of pride.
Reply to Objection 3. The desire for knowledge resulted in our first parents from their inordinate desire for excellence. Hence the serpent began by saying: "You shall be as Gods," and added: "Knowing good and evil."
Reply to Objection 4. According to Augustine (Gen. ad lit. xi, 30), "the woman had not believed the serpent's statement that they were debarred by God from a good and useful thing, were her mind not already filled with the love of her own power, and a certain proud self-presumption." This does not mean that pride preceded the promptings of the serpent, but that as soon as the serpent had spoken his words of persuasion, her mind was puffed up, the result being that she believed the demon to have spoken truly.
Source: Summa Theologica (New Advent)