Is there any pan in which water or liquid shouldn't be boiled?

A picture would help also!

If your pan has a non-stick coating that is flaking off... I'd recommend to discard it. The non-stickness is compromised and the non-stick stuff is probably not good to eat. That said, in my experience non-stick coatings are sensitive to scratching from utensils... not so much from the food itself. It certainly depends on the non-stick material: e.g., PTFE, enamel, ...

Sounds like you're mostly interested in your aluminium pan, but also for posterity...

Cast iron requires some ongoing care and feeding. Boiling or cooking certain things in certain ways can cause cast iron pans to lose seasoning. For example, acidic foods or very wet things without fat will tend to degrade the seasoning, leaving you with a pan that's less seasoned and perhaps with some of the "seasoning" and/or metallic taste transferred to your food; it might not taste as good, and future cooked food will tend to stick more. For example from Lodge, recommendations for foods not to cook in cast iron.

EDIT:

We've come a long distance from the literal meaning of your question. I'll focus on your comment and picture.

It looks like your pan is aluminum, coated with PTFE (brand name "Teflon®") or some similar substance. If I'm correct, your pan is probably very light and heats quickly. It also looks like the pan/coating is badly scratched, and perhaps the coating is peeling off. This means that you're eating small bits of plastic, and the non-stick nature of the pan won't work as well. If it were mine, I'd discard it and never buy anything like it ever again. :) There are plenty of products out there that have more resilient non-stick properties, from well-seasoned cast iron to manufactured coatings.

MORE:

• As to safety and uses, DuPont^TM itself gives answers to some questions about its brand. That says that boiling (e.g., water) in nonstick is not harmful. So, it sounds like you can boil things in it. That said, PTFE is actually a rather good thermal insulator (~500x worse than aluminium, for example). This seems undesirable for boiling something, when bulk heat transfer is what you seek. It may not make much difference because the coating is so thin, but low thermal diffusion suggests to me that boiling water in a bare metal pan will be more efficient, though a quick search doesn’t seem to be conclusive. Not my choice, but YMMV.

• There are many recommendations of what not to do with your non-stick pan, such as this one. Depending on what you’re boiling there may be a recommendation against it.

According to The Food Lover's Companion, Fourth Edition, (2007) definition of cookware and bakeware materials, neither untreated copper nor untreated aluminum should ever be used for food storage or preparation. But it does go on to say that

most copper and aluminum cookware is lined with a nonreactive metal (stainless steel) to make it usable with all foods,

thus making it safe so long as that lining remains in tact. In short, since you can detect that the lining of your pan has been compromised the pan should not be used for boiling or for any other form of cooking. Unlike copper, which according to the text can actually release a verdigris toxin, the problem with the use of untreated aluminum cookware is its ability to wreak havoc on the cosmetic appeal of certain foods. It will cause discoloration in dishes

containing eggs, wine, or other acidic ingredients.

And though it does not speak to any specific health concerns which may follow from the use of untreated aluminum cookware, (Here's an article which explains why that would be omitted), it does make clear that the superior aluminum cookware has undergone an electrochemical process called anodization which makes it extremely hard, low-stick (but not nonstick), and safely nonreactive to food acids unless one attempts to use them for food storage.

Ironware too, it says, is highly reactive with certain foods and must either be seasoned or enameled (aka La Creuset) to prevent of such problems. (Many of us sware by cast iron cookware as preferable to all else for most things.) It is interesting to note also that

light-colored enameled surfaces don't brown food as well as those that are dark and will also eventually discolor with use.

Mention is given of nonstick cookware and the fact that less expensive varieties can flake off over time. And while it does not speak to the matter of biochemical safety for such products as Dupont Teflon, the fact that only through overheating can toxic gases be released is established by chemist Dr. Robert Woke in his book What Einstein Told His Cook: Kitchen Science Explained, (2008).

The definition essentially closes out saying,

The best of all possible worlds is clad metal stainless cookware with a core of either aluminum or copper (both are excellent heat conductors) sandwiched between two thin sheets of stainless steel.

Acid foods such as tomato sauce or egg-lemon soup will corrode aluminum. If your non-stick coating is damaged it will expose aluminum to that corrosion. That can cause the remaining nonstick coating to begin flaking off. Aluminum also reacts vigorously with basic compounds such as sodium carbonate or calcium hydroxide. That makes aluminum a poor choice for nixtamalizing corn.

The scratch in the teflon coating of the pictured aluminum pan makes a perfect entry point for corrosive acids or bases. Depending on use, it'll likely take a year or so, but the teflon will begin to flake from the surrounding area. Your pan is doomed, but as long as you avoid harsh conditions it has a while yet to go before it needs replacement.