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Because the real situation looks a lot more like this:

Your pen is (presumably) not made of mirror-like polished metal, but rather of something like wood or plastic that reflects light diffusely. This means that the light from each part of the pen is scattered all over the paper (and, of course, in other directions too), so it won't project a clear image onto the paper.

(And since the paper itself is also a diffuse reflector, all the light that hits it gets scattered in all directions again, and some of it ends up hitting your eye. If you replaced the paper with a mirror, then only those rays that were coming from just the right direction would have a chance of getting reflected towards your eye, and so you'd see a sharp reflected image.)

OK, so why won't the pen at least form a blurred image on the paper, then? Well, actually it does.

Here's a photo I just took with my cellphone. Sorry that it's a bit dark, I wanted to make sure I didn't burn out any highlights.

If you look closely and carefully, you can see just the slightest hint of yellowish color on the paper near the pencil, and a hint of red near the pen. Those faint colors are caused by light reflecting off the pen and the pencil onto the paper. But they're not very bright, because most of the light hitting the paper is still coming from other directions (primarily, from the lamp illuminating the scene), and not very distinct, because the light that does reflect off the pen and the pencil gets spread in all directions.

Just in case you can't see it clearly on your screen, here's the same photo with the color levels adjusted for maximum contrast:

There, I bet you can see it now. It almost looks as if the pen and the pencil were glowing... which, of course, technically they are. Not with their own light, of course, but with light reflected from the lamp that illuminates them, just like e.g. the moon glows with reflected sunlight.

As a bonus, if you look carefully, you can also see some brighter spots on the paper near the pencil. Those are specular reflections from the glossy print on the pencil. So we actually have both diffuse and specular reflection demonstrated in the same picture.

You will not see a real image of the pen forming on the paper, nor will you see a virtual image from the reflection of the pen from the paper.

The reason you will not see a real image forming on the paper is that the light scattering from the pen is diverging, and in order to see an image all rays from a single point on the pen must converge onto a single point on the paper. That's why placing a converging lens at the right place will form an image.

The reason you will not see a virtual image from reflection is that the reflection from the paper is diffusive and not specular, i.e. the incident rays are scattered randomly instead 'angle of incident equals to the angle of reflection'.

A real image forms when multiple rays from the same point meet at again at another point. Without optical element, the rays just go in their own different directions and don't meet again. So there is no image.

When you put a convex lens in front of the pen, why you can now see the image of the pen on the paper?

Because a convex lens bends the rays so that the diverging rays originating from any given point on the pen—as long as it is further than the focal point—start to converge on the other side. The basic rules say that a ray passing through the centre of the lens passes straight and a ray passing parallel to the optical axis on one side passes through the focal point.

These rules allow you to trace three different rays through the lens and where they intersect on the other side, there is the real image (which you can see iff it coincides with a piece of paper). You could trace the other rays too, but that requires more advanced analytical geometry.

When then can you see the image of a torch when you shine it on the paper?

I you are talking about a real torch—as in a stick with a piece of burning rag wound around one end—you won't. You'll only see a more brightly illuminated spot where the paper is closer to the torch.

If you are talking about the electric kind, most of them are reflectors, that is they have a parabolic mirror mounted behind the light emitting element.

The mirror should be mounted so that the light emitting element is closer to the mirror than the focal point, in which case there is no real image, but a virtual image behind the mirror. Virtual image can be seen directly if the light is not too bright to look directly into it.

However sometimes the mirror is mounted too far from the light element—or can be positioned there in the variable focus lights—and then there is a real image ahead of the light you can project on a paper.

The light scatters off the pen in all possible directions with similar intensity, so one point of the paper is illuminated with scattered light from all points of the pen and one gets a very blurry image. Better image can be got only if somehow the point on paper gets light only from some point or only a small area on the pen, such as when using a lens or a camera obscura: https://en.wikipedia.org/wiki/Camera_obscura

A reflective or polished surface respects and preserves the angular proximity of incoming beams on its points. The less the angular proximity of incoming intensity is preserved in the outgoing intensity profile, the more diffuse and "matte" looks the surface

In a mirror light is highly likely to reflect only in one angle according to the "law of reflection" ( I have no idea of why that is though ). On a paper it is likely to also reflect in all other directions. Therefore, on the paper, the image of the pencil is drowned out from the light hitting it from all other points in the environment. The light from each point on the pen will hit each point on the paper, and thus contribute to diffuse the image of itself.

With a lens, you will only be able to see the image of the pen on the paper, if the only light that hits the paper is coming through the lens, or at least other light is sufficiently dim. Also the lens must be at the correct distance so it will focus all light coming from one point on the pen to one point on the paper. The reason you see a picture in that case, is because for each point on the paper, there is only one point on the pen (or whatever else is out there) as seen from the point of the lens, that will hit each point on the paper. This means that all light reflected from that point on the paper is coming only from one point on the pen.

A torch will send directed light, thus light from one point on the torch only hits one part of the paper. Since the light is a lot brighter than the light coming from the environment, the light that hits your eye, will come from only the one point on the torch, thus recreating the round circle of the torch.

Here are som drawings to illustrate. Blue are the rays that hits the eye, while red misses the eye.

Pen to paper: (light from one point is illuminating all parts of the paper)

Pen to mirror: (light from one point is reflected in only one direction for each incidence angle)

Pen through lens: (the lens bends the incoming light so that for a given distance ratio between the pen and paper, each point illuminates only one point on the paper)

Torch: (directional light illuminates only one point on the paper for each point on the torch)