Issue pressing down French Press

Reasons have already been covered
Grounds too fine
You didn't wait for it to bloom

…however, no-one has mentioned a 'fix'.

Lift the filter out completely & give it one more stir before you press it, that will let any remaining air out. If it still fights you, lift the filter half an inch & press again, several times until you reach the bottom, that will slightly compensate for too fine a grind.

My guess is that you're not waiting for the bloom before you stir.

1. Pour in water about half way.
2. Wait one minute.
3. Stir (it will have bloomed by this point)
4. Pour the rest of the water in.
5. Wait 3 minutes or so and then push down the filter.

It should be really easy even if you grind the coffee fairly fine. I grind the coffee finer than is recommended and have zero issues pushing down the filter.

You will have to learn how to pour the last few sips of the coffee so that you don't inadvertently pour in grinds / sludge.

If you're buying pre-ground general-purpose coffee for French press, the coffee grinds are probably too fine. They will clog your filter. General purpose coffee is ground for drip brewing, and French press uses coarser grinds (partly so you don't get so much sludge in your cup and partly to minimize overextraction from long brew times). The filter is designed for those coarse grinds and will clog with finer grinds like drip.

Avoid this by grinding your own coffee (many grocers offer in-store grinders with bulk coffee) or buying pre-ground coffee in French press grind. Pressing should never require a significant application of force. If you press hard, the pressure can be released suddenly and cause an explosive release of hot water and coffee, like you describe in the question. Minimally very messy and possibly very dangerous.

It's possible that the filter might be clogged, but as I've seen in your replies it sounds like you try to keep up with cleaning it.

If it isn't clogged, it could also be a problem with your grind. Coffee should be ground quite coarse for a french press so the plunger can work properly. I've seen people have coffee shoot out of the top in the past and it's usually because they ground the beans too fine and the water couldn't easily pass through when plunging.

A number of things aren't clear from your question. I can think of three issues that might result in the problem you're having.

Clogged strainer

If the strainer is clogged, the air has trouble being pushed out. That may make it harder to push it down as the air stays under your strainer.

The solution is easy, make sure the equipment is cleaned well, a bit of soap does wonders to remove oily residuals.

Equipment

You may be using large equipment to make a small amount of coffee. That way, when you're pressing down the strainer is already near the bottom of your container meaning you cannot press much further. To solve this, try using a container of an appropriate size. If your French press is filled at least halfway at step 4 then this shouldn't be an issue, if it's much less, consider making a larger batch or using a smaller French press.

Blooming

Blooming is technique for letting gasses (mainly carbon dioxide) escape the coffee beans. I don't think this is what causing you trouble, but I think it's worth mentioning. To get a good bloom, you just need to take some time between step 4 and step 5. After stirring the beans, you wait 30 to 60 seconds to allow some of the gasses to escape.