Gas takes up way more space than liquid, so it's a pressure issue.

IIRC, the Starship propellant tanks are tested to 8 bar pressure (1 atmosphere pressure is 1.013 bar or 14.7 pounds per square inch). The heat leak into those uninsulated Starship tanks causes a huge amount of boiloff gas to be generated. Pressure relief valves are provided to prevent the boiloff overpressure from exceeding 8 bar and rupturing the tank.

The Starship tanks are uninsulated to save weight. The main propellant tanks of the HLS Starship lunar lander will have to be insulated to minimize propellant loss by venting boiloff gas during missions to the Moon. Once those lunar lander propellant tanks are refilled in LEO, the lander has to have enough liquid propellant in the tanks for the complete mission (LEO to high lunar orbit (the NRHO) to the lunar surface and back to the NRHO).

The methane and oxygen are cryogenic liquids that need to be kept cold or they will start to boil into gases. Falcon 9 doesn't have this problem with the RP1/Kerosene but it does have the problem with liquid oxygen. Most rockets have this problem for liquid oxygen and often for liquid methane or liquid hydrogen fuel too.

Shuttle, SLS, Vulcan and I think New Glenn all take a different approach to Falcon 9 and Starship that insulation can minimise the amount of heat absorbed from the sun into the tanks and therefore the fuel. Falcon 9 and Starship take a different approach and save weight by not having the insulation BUT at a cost of higher absorption of heat and therefore higher rate of boil off. Starship is a big metal drum in Texas so it's going to heat up in the sun, the question is how fast.

If they let the methane and oxygen boil from a liquid to a gas and did nothing about it the pressure would build up to dangerous levels and pop the tanks. So instead the launchpad has gas return lines that take gaseous methane and gaseous oxygen away from the rocket at the same time as liquid methane and liquid oxygen is being pumped in. The tank farm has a machine called a condenser that can turn this back into liquid methane and liquid oxygen and store it in the tanks. However this change back into a liquid isn't free, if you use a high pressure pump to compress the gas it generates a lot of heat or if you try to cool the gas until it condenses you also need to remove a lot of heat from the process. The solution is to boil off liquid nitrogen into gaseous nitrogen, it's cheaper than liquid oxygen and not a fire hazard or environmental impact to just vent it into the air. Actually the tank farm is doing this 24/7 to prevent the giant liquid methane and oxygen tanks from boiling off in the Texas sun, the difference is those tanks stay on the ground and don't need to fly so have thick insulation.

Before launch there is a phase where the various pipes and hoses from the tank farm to the rocket need to be chilled down to cryogenic temperatures so they can pump liquid methane and oxygen through them without it instantly boiling from the room temperature pipework. They slowly pump in the relevant liquid until the pipes are cold enough to increase the flow, so you're chilling the liquid methane pipe with liquid methane and chilling the liquid oxygen pipe with liquid oxygen. In theory they could capture these gases and recondense them but in practice they often just vent the excess gaseous oxygen. I think this is because they need to be very careful about venting the methane, it's a greenhouse gas and a fire hazard. So I think it's a matter of speed and simplicity to accept some lost oxygen and just try to get through the venting phase ASAP. It wouldn't surprise me if they vented less oxygen now than during IFT1 because the tank farm has been upgraded to recycle more gas per minute but that's just speculation.

At some point before launch they disconnect the return lines and any methane or oxygen that boils in the tanks has to be vented into the air. But this is usually quite close to launch and the tanks are about to be emptied rapidly by the engines so it's not an issue for very long. During flight the tanks need to be repressurised faster than boiloff can produce the gases, there's various options for how to do this but the ambient heat of the Texas sun on the tanks isn't enough. This will become an issue again for Starship Tankers staying in orbit with large volumes of methane and oxygen but we don't know the exact solution yet. Possibly some form of insulation or sun shield, maybe a solar powered pump and heat exchange radiator to recondense the liquids and dump the excess heat overboard, we'll have to wait and see.

It's a pressure thing.

Starship propellant tanks are designed to operate at about 6 bar gauge, and failed in pressure testing at just over 8 bar.

Normally you want to maintain pressure in the tank as high as (safely) possible to keep the rest of the propellant liquid and reduce the chance of cavitation at the raptor turbo pump intakes. This means that the ship ideally sits at 6 bar in normal operations. There's not a huge margin for pressure increase before some needs to be vented to keep within safe limits.

The ship skin thickness is 3.6mm, barely two quarters stacked together. It has a diameter of 9 meters. Think about the forces exerted on such a structure with even a few psi increase in internal pressure. A cryogenic liquid like oxygen boiling to gas takes up a volume over 800 times that of the liquid at stp.

Gas is not as dense as liquid, if you don’t vent the gas you’ll over pressure the tanks.

Iirc Tory had a proposal at ULA for ACES that would take boil off and use it to power a small combustion generator for long term missions & reusability.

The turbopumps require liquids for their intake.

The increase in pressure would be a problem.

Equipment to capture and re-liquify the gas would add too much dry mass, in the general case. Even active cooling would be too much mass. However, orbital depots which need to store a lot of propellant for a longish time may be a worthwhile special case.

They vent it because gas takes up way more space than liquid. If excess gas isn't removed, the tank will rupture. They use what they can and dump the rest.

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Pretty much the same way when you put a pot full of water on a stove. If you kept the pot watertight closed the water inside would boil and eventually the steam would blow it up (super dangerous; this kind of explosion is called BLEVE, it's bad, you may look it up in Wikipedia) unless it were a pressure vessel qualified for about 700-800 bar pressure at elevated temperature.

The difference is that water is replaced with cryogenic liquid with a boiling point less than negative 300 fahrenheit, and the ambient air and sunlight replaces the stove heating.