"I can't get sunburned on cloudy days."
Even on cloudy, hazy days, 70-80% of the sun's ultraviolet rays reach the ground.

"I have a tan so I'm safe in the sun."
Any time skin darkens, it is trying to protect itself from the damage the sun is inflicting upon it. There is presently no way to stimulate the skin to increase its pigmentation without damaging it first. Over time, tanned skin turns into prematurely wrinkled, leathery, sagging skin that has an increased risk of developing skin cancer.

"I am wearing a shirt so I don't need a sunscreen."
A light-colored t-shirt, wet from sweat or water, transmits almost as much ultraviolet radiation as no shirt at all.

"If SPF 30 is good, SPF 60 must be even better."
SPF 30 blocks 96.5% of UV rays. SPF 60 adds less than 1% of protection (97.4%) but adds significantly more active ingredients which can be harsh to the skin and might cause allergic reactions.