I find it very confusing when people say that the strength of the magnetic field is proportional to no. of field lines/area. Why is this terminology still used?
The terminology is still used because it is correct and it gives a graphical way to understand magnetic fields that is particularly intuitive to understand and apply.
For an example, consider the set of all lines in the plane passing through the origin and through the vertical line segment $x=1$ and $y=[0,1]$. There are an uncountably infinite number of points in that segment and a unique line for every such point. There are no gaps or missing points.
Now consider the set of all lines passing through the origin and the vertical line segment $x=2$ and $y=[0,1]$. Note that there is also an uncountably infinite number of points in this second segment and a unique line for every such point in the second segment. There are again no gaps or missing points.
Now, consider the relationship between these two sets of lines. All of the lines that go through the second segment also go through the first, but the reverse is not true. Half of the lines that go through the first segment do not go through the second. Therefore, indeed the number of lines through the second is less than the number of lines through the first. Half of an infinite number of lines is still an infinite number of lines, so the cardinality of the set is unchanged (infinity is weird).
No gaps have opened up, but the number of lines through the second segment is, in a physically valid sense, half the number of lines through the first segment. Sometimes the ratio of two infinite quantities is finite. Of course, we cannot draw every such line, but we can draw a representative set of a few and convey the concept of the whole field of lines. Doing so allows us to correctly and intuitively reason about the behavior of the field in a way that is difficult using the integrals directly.
This is the sense in which the strength of the magnetic field is proportional to the number of field lines/area. There are an infinite number of lines through each area, but some of the lines going through one area do not go through another. The proportion of lines that miss the other area is the proportion that the field strength decreases.