A possible motivation is hinted at in the scene where Morpheus calls Neo at his workplace (the very first time they speak).
MORPHEUS: Hello, Neo. Do you know who this is?
MORPHEUS: Yes. I’ve been looking for you, Neo. I don't know if you’re ready to see what I want to show you, but unfortunately you and I have run out of time. They're coming for you, Neo, and I don't know what they're going to do.
The idea that they've run out of time -- and that that's unfortunate -- implies that Morpheus would've preferred to have postponed Neo's extraction from the Matrix for even longer than he did, and that something made him feel compelled to proceed with that earlier than he wanted.
Morpheus directly following up that statement by saying that the Agents were coming for Neo, and that he didn't know what they were going to do, implies that that specifically is what made him feel compelled to free Neo earlier than he wanted.
That still leaves the question of why precisely Morpheus didn't want to free Neo as early as the night that Neo and Trinity met in the nightclub, which brings us to the part about Neo not necessarily being ready to see what Morpheus wanted to show him.
Later in the film, there's a scene where Morpheus indicates that it's dangerous to free a mind as old as Neo's, since people over a certain age have trouble letting go of the Matrix.
NEO: I can't go back, can I?
MORPHEUS: No. But if you could, would you really want to? I feel I owe you an apology. We have a rule. We never free a mind once it's reached a certain age. It's dangerous, the mind has trouble letting go. I've seen it before and I'm sorry. I did what I did because... I had to.
We saw this in Cypher, who clearly resented Morpheus and his crew for having freed him from the Matrix, to the point that he was willing to literally kill them to get back into the Matrix.
CYPHER: I'm tired, Trinity. I'm tired of this war. I'm tired of fighting. I'm tired of this ship, being cold, of eating the same goddamn goop everyday. But most of all, I'm tired of that jack-off and all his bullshit. Surprise, asshole! I bet you never saw this coming, didja? God, I wish I could be there, when they break you. I wish I could walk in just when it happens. So right then, you'd know it was me.
TRINITY: You gave them Morpheus.
CYPHER: He lied to us, Trinity. He tricked us. If you'da told us the truth, we woulda told you to shove that red pill right up your ass.
TRINITY: That's not true, Cypher, he set us free.
CYPHER: Free? You call this free? All I do is what he tells me to do. If I had to choose between that and the Matrix, I choose the Matrix.
To a lesser extent, we arguably saw this in Neo as well; when Morpheus finally explained to Neo what the Matrix was (in the scene in the Construct), Neo had a little bit of a mental breakdown, and expressed feelings of distrust towards Morpheus and his crew.
MORPHEUS: What is the Matrix? Control. The Matrix is a computer generated dream world built to keep us under control in order to change a human being into this.
NEO: No. I don't believe it. It's not possible.
MORPHEUS: I didn't say it would be easy, Neo. I just said it would be the truth.
NEO: Stop. Let me out. Let me out! I want out!
TRINITY: Easy, Neo. Easy.
NEO: Get this thing out of me. Get this thing out of me! Don't touch me! Stay away from me! I don't believe it. I don't believe it. I don't believe it.
Being freed from the Matrix must be a profound event on a psychological level -- it essentially involves having your entire view of reality turned upside down -- and, evidently, it can go badly wrong if an individual's extraction isn't handled with care.
Given that Neo was both older than was preferred for the purposes of extraction, and not just any ordinary individual, but someone whom Morpheus believed to be the potential saviour of mankind, it makes sense that Morpheus would've wanted to handle his extraction with utmost care, taking as much time as needed to help prepare Neo, mentally, for the ordeal he was about to go through.
There's also the matter of trust. Morpheus and his crew didn't seem to want to force Neo into anything. They wanted him to voluntarily go along with everything they asked of him, including the swallowing of a pill that could've been poison for all he knew. This required considerable trust on Neo's part, and he might've found it harder to trust them if it seemed like they were trying to railroad him into something the very first time that he and Trinity met.