First of all you need to understand that Scully is a skeptic and a scientist. It is by no means uncommon for people to believe in science to a point of it being almost religious. She believes that everything can be explained in some manner through scientific means. I am not going to go into detail of every experience she has had up to that point in the show where she has seen something and refused to believe it since it would be a very long answer and also, to be perfectly fair though, you haven't exactly established that she doesn't believe in any of those specific items after having experienced them first hand. In other words, seeing a woman levitate doesn't prove every other paranormal phenomenon including the existence of aliens. Since the existence of aliens is a recurring theme in the show however, it does make sense to take a look at just how much first hand experience Scully has with aliens.
So let's review just how much actual first hand evidence Scully has of aliens by the beginning of season 3 since that is the specific point you mention in your question.
The following is a list of episodes from Season 1 and 2 that deal with aliens. I've been somewhat liberal in what qualifies as an episode dealing with "aliens" and this list goes beyond what most would consider mythology related episodes. I also ask that you forgive me if I leave anything out as I didn't have time to go watch all 18 episodes again, but I have seen them all at least 5-6 times if not more so I'll do my best. I should point out that over time Scully does slowly become exposed to more and more evidence to support the existence of aliens and eventually she does become convinced of their existence.
What are some of the stronger items of evidence that Scully actually witnesses or experiences?
- Pilot: time loss in the car and the implant in the fake Ray Soames
- Deep Throat: flashy light things in the sky
- Conduit: nothing
- Space: nothing
- Fallen Angel: nothing
- Gender Bender: crop circle
- E.B.E.: nothing; if anything this episode convinces Scully that all the evidence of aliens are actually an elaborate hoax being used as a
- The Erlenmeyer Flask: purity control substance containing alien DNA, and the alien fetus
- Little Green Men: nothing
- Duane Barry / Ascension / One Breath: she is abducted but she has no memory of her abduction
- Colony / End Game: possible clones, more alien fetuses, and the alien bounty hunter
- Fearful Symmetry: nothing
- Anasazi / The Blessing Way / Paper Clip: more evidence of government conspiracy but nothing to point to irrefutable evidence of
Longer listing with summaries
Scully's only firsthand experience with aliens in this episode comes with the time loss experienced by her and Mulder in the car and the unidentifiable implant from the corpse they dig up from Ray Soames' grave. Being this is the first experience she's had with these things she is understandably skeptical when Mulder claims that the flashes causing the time loss was due to aliens. I believe one of the explanations she thinks is that the car was struck by lightning. As for the implant, she doesn't refute that it is a peice of evidence that needs to be investigated. Also its important to note that she becomes a pretty solid believer that there is some sort of government conspiracy from the very beginning.
Deep Throat -
The only evidence of aliens that Scully witnesses first hand in this episode is the UFOs which only appear as lights flashing across the sky. She is not able to identify that they are of alien origin, all she knows is that they witnessed some strange aircraft over a top secret airbase so its not unreasonably explained as experimental aircraft using earth technology and there is no solid evidence to suggest aliens.
To the best of my memory, Scully witnesses nothing first hand in this episode and has a reasonable alternative explanation for any of the strange findings such as the burned trees being the result of an electrical storm and not a UFO. I should also mention that they have pretty solid evidence in the episode to suggest that the girl Ruby was abducted not by a UFO but by a jealous boyfriend.
This is one of those stretch inclusions since the episode isn't really about "aliens" in the traditional sense of little green men. Again this episode doesn't have Scully witnessing the existence of aliens firsthand in any way.
Fallen Angel -
Scully doesn't even show up in this episode until she arrives to bail Mulder out of military prison for trespassing on a top secret crash site for which she has been given a perfectly reasonable explanation that it is a downed Libyan jet with a nuclear warhead and not a UFO. Scully does not witness any paranormal phenomenon in the episode.
Gender Bender -
Another stretch inclusion as the alien factor only comes into play at the very end of the episode where it is revealed that the Amish-like group has disappeared from their village and left a crop circle. I will only say with this one that there is no firsthand evidence of aliens. A crop circle can be explained away.
It is established early in the episode that none of the evidence of aliens in this episode is conclusive. Once again we have an episode where Scully doesn't witness anything paranormal. In fact the evidence in this episode points to government conspiracy and that their source Deep Throat is in fact feeding them fake evidence of aliens. Before you argue that Scully and Mulder did in fact witness first hand an alien in the back of the truck at the end of the episode, I urge you to reconsider the scene in which Mulder himself tells Scully that what they witnessed was in fact another elaborate hoax.
The Erlenmeyer Flask -
Keep in mind that the last time they dealt with a case based on information from Deep Throat they determined all the clues they were given were hoaxes. That includes Mulder. This episode does give us finally some pretty solid scientific evidence that Scully can not refute of extra terrestrial life. The first comes in the form of the purity control substances which after various tests is revealed to contain extra terrestrial DNA. Scully's reaction to this shows that she has at least begun to let the barrier be broken in that she is willing to accept that this could in fact be true. She is stubborn however and even when she reports these findings to Mulder her verbiage indicates that she still only thinks that the stubstance "could be extra-terrestrial". But then when she arrives at Mulder's apartment she admits to him, "I just want to say that I was wrong." Later Scully breaks into a lab where she obtains an alien fetus although she is never given the opportunity to examine or do tests on it so there's no way to know that its not just another hoax.
Little Green Men -
In this episode, Scully hasn't denied any of the evidence she's seen. She and Mulder are still taking precautions and keeping their eyes open for more evidence of a government conspiracy, but being separated and having the X-Files closed has limited Scully's exposure and involvement with anything paranormal. This episode is mainly about Mulder and Scully's only involvement is that she shows up to rescue him from Arecibo.
Duane Barry / Ascension / One Breath -
I'm putting these into one because they are all related to the same microarc. Duane Barry episode almost entirely deals with a hostage crisis with a man who claims to be an alien abductee. Scully at the end of the episode discovers the implant in her neck and sees how it sets the cash register to go bonkers. She is then abducted by Duane Barry himself who takes her to a mountain so she will be abducted in his place. She is. And two episodes later she is returned mysteriously and is in a coma for the entire episode of One Breath. So what is her first hand experience here? Well she was abducted by aliens! Of course! But... she has no memory of this when she is returned. All she knows is that Duane Barry took her and she was missing for a while and returned. There is no evidence of who actually took her all that time. Not even Mulder has concrete evidence of her having been abducted by aliens.
Colony / End Game -
Another miniarc. This series begins based on an anonymous tip, of which Scully is understandably skeptical as she puts it because "we've been setup before". This episode gives Scully first hand experience with men who are reportedly clones (although there are such things as identical siblings so this is hardly concrete). She does see some test subjects in tubes in a lab but this is hardly anything new as she's seen the alien fetus before. The cliffhanger between episodes shows her face to face with the shape shifting alien bounty hunter who looks like Mulder, while she is on the phone with the real Mulder. This is her first experience with the shape shifter and she never denies his existence. She clearly doesn't believe he is an alien though and there's no proof that he is. As far as she knows he is a man who has a clever disguise.
Fearful Symmetry -
This episode deals with animals being abducted by aliens but there isn't any firsthand experience from Scully of aliens.
Anasazi / The Blessing Way / Paper Clip -
Scully's experiences in these episodes are limited to more of the same. Findings of evidence of a government conspiracy and possibly an alien hoax as a cover up but nothing solid and irrefutable.
By the end of Season 2, there are only a few items that Scully has witnessed first hand that have been scientifically verified to show the existence of extra-terrestrials and she has denied none of these after having seen them. Everything else has an alternative theory which is perfectly viable AND there is actually more experiences to point to any alien involvement being a hoax perpetrated by the government as a cover up of a larger conspiracy. So there's really no reasonable expectation that Scully would simply abandon her beliefs and experiences at this point to simply accept any hair-brained and unsubstantiated theory that Mulder throws out as gospel truth.