Flat tire light?

It can depend on were the sensor is located. In the value stem, the sensor has dirt in it or gone bad, in the caliber, again dirt or sensor has gone bad.  I had that with my Jeep and it was because the cap on the value was crossed threaded.  Try washing all four wheels off and see if that helps and ask your local tirer dealer what type of sensor you have. It can be an easy fix for a few bucks or if the sensor is bad that can COST MUCH -O-!.  

Low tire pressure may cause the tire pressure light to flash. If this is happening, the first thing you should do is pull over safely and inspect your tires. Use a tire pressure gauge to check that all four wheels are at specification. Use a tire inflator to bring any underinflated tires to specification or replace the tire with the spare.

2013 Accord infers the tire pressure from the ABS sensors, no magical tires needed. Make sure your tires are inflated correctly, find the TPMS button under the dash and hold it until the light blinks twice. It should figure your tires out after 20 minutes worth of driving 30 to 60 mph. Do that any time you make a change or adjust the pressure.

It's nothing to do with any tires needing to be replaced. It's a pressure monitor. If you checked the pressures yourself and found them to be low then inflating them to the correct pressure will have rectified the problem.  Now the monitor system needs to be reset, how you do this on your car I don't know.  Read the handbook or look it up on line.

It may be that this doesn't sort it out, in which case you have a faulty sensor.

These things cause more trouble than they're worth. Personally I check with a pressure gauge on a regular basis.

2013....likely the batteries in the sensors are dead or weak. There's a computer that can read the monitors with the wheels still on the car. Autel makes a TPMS reader for $50-$70. The Bartec computer costs quite a bit more, but it can reset or program monitors. The guy at Big O tires checked mine with his Bartec computer for free....batteries were dead ( 2010 Corolla). Easy sense monitors are crap, ifyou're looking to replace them. Dorman TPMS monitors are great and cost less than OEM. You still have to break down the tire to install the monitor.

if the tires are holding pressure then you have a faulty valve pressure switch .. one of the sensors is at fault , could need an auto-electrical technician

It means you need to read about the TPMS system in your vehicle and find out if the light needs to be reset. Another possibility is that the batteries in the tire pressure transmitters may be depleted/dead and you need new tire sensors installed. I prefer putting black electrical tape over the light and checking my tire pressures with my tire gauge every 2 months. Sure beats paying $400 to get the TPMS system working again. 

Replace the batteries. 

I think your dad is totally wrong.  Did you check the pressure of the spare tire ?

the battery in one of the tyre pressure sensors is probably flat