In fact, the probe particle has to have very large momentum to have smaller wave length than the size of particle/ nucleus to be probed. Some time mode of interaction also become basis. As thermal neutron having high magnetic moment can provide revealing results on magnetic interaction.

Well, I can offer an intuitive answer:

Imagine that you're blind, and numb, and you want to know how big something is.

The doctor provides you with a special stick that beeps when it hits something.

You can easily do things like get a sense of how big a door or stove is with the stick by poking around, listening for the beep, moving the stick, and poking around again until you hear the beep.

But, when it comes to determining something like the size of a sewing pin, it becomes difficult.  You can't be sure which part of the stick is contacting the pin. the stick is large with respect to the pin.

If, however, you are given a very small stick - on the same scale as the sewing pin, this sort of task becomes easier.  You're able to get a much clearer sense of the dimension of the pin, since you can more precisely know where your small stick is contacting the pin.

You will not be  never able to cut an orange with the another one. You wiil smash both of them!

You can also calculate errors in measurement if size of probe is smaller or bigger than the size of particle to be probed.

As previously said, it's a question of wave length.

Imagine an object in the water waves (rock, stick). If you have a large wave (in term of distance between two maxima), it will go around your object without any perturbation. If you have short waves (especially shorter than the size of the object), the object will reflect the wave.

In nuclear physic, if your probe particle has a very large wave length, it cannot "see" particles with very short wave length.

Another way of looking at it is that the reaction will depend on the structure of both the probe and the target.  If the probe is point-like, i.e. has no structure, then you are cleanly studying only the structure of the target.  This can't always be done, but if one particle is much smaller than the other, then it's structure effects may be smaller, giving you a pretty good probe of the structure of the larger object.

Of course, it's not strictly size that's relevant, as mentioned in some of the previous answers, but it's a reasonable shorthand in many cases.

It is not just the size of the particle that is used to probe the nucleus but its de Broglie wavelength.  The smaller the de Broglie wavelength, the greater is the resolving power.  To probe the interior of the nucleus, you require a probe with greater resolving power or a probe that can scan smaller and smaller spatial regions.