Cancers can cause death in more than one way. So there is no single answer to this question. It really depends on the type of cancer you have and which parts of your body are affected.

Other people have covered the effects of solid tumors quite well.

Blood tumors often do not form solid masses. They are the result of stem cells in the bone marrow (or occasionally actual immune system cells) becoming cancerous. These cells are highly mobile and usually do not embed themselves in solid tissue (except for lymphomas). What they do is outcompete your normal bone marrow and blood cells, preventing your immune system from working and your red blood cells from regenerating and your platelets from clotting your blood. I've read reports from autopsies in the 1800s of people who died from (what we would call untreated) leukemia that their blood resembled pus more than blood due to the paucity of normal red blood cells and huge level of abnormal nonfunctional white blood cells.

• Cancerous cells multiply incontrollably until they form their little own neighborhood, called tumor, which slowly and ruthlessly pushes everything else out of its way. In the case of lung cancer, the obvious consequence is that there's less space available for the healthy lung to do its job.
• Cancerous cells are ravenous consumers of resources, and compete with the host body for them. You slowly become emaciated and malnourished as your cancer steals your food from you.
• Tumors arising in glands may result in the dangerous overproduction of certain hormones.

I read somewhere that a primary cancer seldom kills ; most of the time the metastasic-induced does. Why ? There should be far more "bad" cells in the primary site, doesn’t it ?

In the West you can often operate the primary site away.

I read somewhere that a primary cancer seldom kills ; most of the time the metastasic-induced does. Why ? There should be far more "bad" cells in the primary site, doesn’t it ?

The most anatomical origins for cancers (skin, breast and prostate) are not vital organs, so a cancer in one of those places won't kill you if it stays in place. The danger is if it metastasizes to a vital organ (most commonly the lungs or liver) and interferes with its function. If a cancer starts in a vital organ, it's more likely to kill you through its effects on that organ, not by spreading elsewhere.

I'm not particularly knowledgeable about cancer but I can give you the simplified version:

few additional cells

I think this is at the root of your misconception. It starts out as a few additional cells rapidly dividing, but the end-stage typically involves macroscopic-level changes, like this Here.

Sometimes it's the sheer bulk of cells that kills in the same way a rock in your brain might, other times it's the gradual replacement of working cells with non-functional cells, and other times it messes up sophisticated signalling stuff. (For example, the cancer cells might be putting out large amounts of hormones, or diverting blood flow).

primary cancer seldom kills ; most of the time the metastasic-induced does. Why ?

Metastatis means little cancer "seed" cells are floating around all over your bloodstream, right? This means that at any random time, a cancerous growth can suddenly pop up in any random region with no warning. Some of these growths will be benign, and others deadly. You have to obsessively scan the body for new growths from then on if you want to protect yourself.

With primary cancers at least you can sometimes just cut them or irradiate them or shrink them, or just work around them (like with lung cancer, just give them an oxygen tank to make up for the reduced efficiency).

To throw another reference into the discussion, section 1.8 of McKinnell et al.'s The Biological Basis of Cancer spends a few pages on this. Summary: cancers can cause organ failure, but because the body has "an enormous reserve of normal tissue plus a built-in mechanism to regenerate more" organ failure is not usually the proximate cause of (edit: non-leukaemia) cancer death; the most common cause of death is instead cachexia (wasting) and hence infection.