Qfyilyi

This is the headline of an online article:

Tasty Fish Grow Smaller in Warming Ocean.

And this is from Google search:

Why Belgian coins grow smaller.

Growing is all about increasing in size and getting bigger while smaller is just the opposite, however, English seems to permit the two words to come together.
How is this possible?

Grow and smaller aren't linked the way you are interpreting it. The sentence is saying that fish that used to reach a certain size in adulthood aren't growing that big in a warmer ocean, they are smaller than their predecessors.

Oxford lists three primary meanings for the word grow. The first two reflect what we often immediately think of when we think about growing:

grow (v.) to undergo natural development by increasing in size and changing physically

grow (v.) to become larger or greater over a period of time; to increase

It’s the third meaning, though, that provides the key to your apparent oxymoron:

grow (v.) to become, gradually or increasingly :
sharing our experiences we grew braver

So, if the number of fish are gradually becoming diminished, then a headline might say:

Tasty Fish Grow Smaller in Warming Ocean

More likely, though, is probably referring to the size of the fish, if the gradually-warming ocean is causing the fish to become smaller over time (or, perhaps more accurately, "causing the average size of adult fish to become smaller over time").

As well as the common usage of grow to increase in size it can also be used to indicate a gradual or progressive change of state for example

As night fell it began to grow colder.

Having said that using the phrase 'grow' smaller is probably best avoided as it is a bit ambiguous as it is not clear whether it means they actually shrink or they just grow more slowly, reach a smaller maximum size or indicating a trend in in the population as a whole over time.

Although this is often the case with headlines and often the ambiguity is deliberate in order to make a story sound more interesting or sensational than it really is.

I don’t see any conflict in it.

Yes, “to grow” means get bigger and they are! but consider that they grow less than expected.

Tasty Fish Grow Smaller [than it is expected] in Warming Ocean.

I think you can use 'grow', since there is an increase of 'smallness' compared to a previous state. A different argument is: 'grow smaller' does not mean a big fish turns small. It just means that fish now have a slower growth rate, or that they stop growing earlier at all. Nevertheless you have the act of 'growing' from tadpole to fish. This is what 'grow' refers to, it is not a general phenomena that happens to all fish.

So, long and thanks for all the fish :)

What you are referring to is the basic form of speech that we use informally but is not correct ."Things can shrink smaller" is the correct usage .Also sometimes "grow smaller" can be used as an oxymoron in a poem .