1: I am not sure the earthquake is needed in the logline since is just seems to be the setup.

When an apartment complex is is infested with fast breeding spiders.
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2: Why is this apartment complex important to the lead character?

When his arachnophobic mother’s apartment complex is infested with fast breeding spiders
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3: Fast breeding isn’t gripping.

When his arachnophobic mother’s apartment complex is infested with deadly fast breeding spiders
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4: ‘Young’ is probably the worst way to describe a character since it tells us next to nothing about them.

When his arachnophobic mother’s apartment complex is infested with deadly fast breeding spiders, a wanna-be entomologist must…
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Finally I am not seeing a written connection between forcing someone to move out and saving the complex. Will the spiders suddenly go away when the veteran moves out?

Hope that helped, good luck with this!