Other answers have noted approving an election now would give Johnson greater control over Brexit, and the Conservatives' long-term power, than would refusing it. I'd just like to mention one other issue, one concerned not with Brexit but something arguably more important than that specific policy area.
In December 2018, his predecessor faced an attempt to oust her as Leader of the Conservative Party. There was a question here about that too; and, like this one, it warranted a number of different points, my own being that she'd made one attempt too many to limit Parliament's power. Johnson is now the second Prime Minister in a row to come to power through the Conservative Party's leader-choosing rules instead of a general election, and while that doesn't guarantee he'd play fast and loose with the separation of powers at their expense, it's a prospect that's been on their mind because of Theresa May.
So, what has Johnson done since he became Prime Minister? He's made clear, to a Parliament that has repeatedly voted against a no-deal Brexit, he intends to meet the October 31 deadline whatever it takes, which almost surely means violating Parliament's will (after all, they repeatedly voted down the deal Theresa May secured with the EU, too). Now, that could just be electorate-impressing bluster; he could have meant "whatever it takes, except disregarding laws, or principles of democracy". But it's strike 1.
If Johnson did want to ignore the separation of powers, the easiest way to keep to the deadline would be to stall for time, since as far as the EU is concerned, if Parliament makes no decision the UK leave then anyway. Well, he recently acted to ensure Parliament will be powerlessly prorogued, starting from any day now until almost the deadline. He might not want to abuse his power, but if he did, isn't that basically how he'd act? His defence was that Parliament's proroguing has been postponed quite a bit already. But he could have avoided all suspicion with a November proroguing, so if you're in a suspicious mindset, that's strike 2.
OK, but maybe that was just a careless mistake of his. Surely he wouldn't threaten any Conservative MP who votes against him, which is a big no-no, before his first vote as PM? Surely he wouldn't say he'd break the law to meet the deadline? (In front of police, no less.) I think some have given up counting strikes at this point.
So let's say you're an MP who fears Johnson may care even less about the separation of powers, and rule of law, and everything else Parliament cares for, than Theresa May did. That has to be a common if not universal concern in the chamber. The last thing you'd want to do is let the Prime Minister use one of his office's most historically manipulable powers, that of having an election whenever they'd get the most seats. That would be an especially worrying thing for Johnson to manage now, since it would throw away the existing Parliament, and potentially give him both more Conservative MPs and more pro-no-deal-Brexit MPs. Guess how that prospect makes current MPs feel. As with proroguing, he couldn't have chosen something more suspicious than the October 14/15 suggestion, all while saying (unconvincingly if you're already worried about all this) that he doesn't want an election. (Well, apart from, say, November 1, but they may fear he's purposely doing the second most suspicious thing.)
Limiting Johnson's options doesn't just make tyranny less likely, it makes the not-quite-tyranny stage at hand easier to control. Could Parliament get concessions from Johnson? Well, they've already got him to say he would abide by the law after all. They're not sure enough he's telling the truth not to take some precautions (ibid.), but it's a start.