There are several claims of quite different grades here.
1) Microchips can be removed without death.
Here is a case study.
Here is some legislation describing who is permitted to do so and what administrative action is required.
Note: Based on stories I found on the net, it is difficult to find an vet who is willing to perform unnecessary surgery on an animal.
2) The chip can't be used to track the location of its wearer over long distances.
RFId tags have limited ranges. (e.g. around 40' or 12m, depending on the conditions.)
This isn't like the movies where it can be picked up by satellite. You need to have a sensor very near the device to read it.
That still means it is plausible to have a sensor near, say, a cat-flap to detect whether a cat is in a particular area. Example
3) You can't meaningfully track the owner from the pet's chip.
Unless the animal is a guidedog, the owner is generally not with the animal at all times. [Reference: Common knowledge about pets being left home while owners go out, and cats going out while owners stay home.] Even if you could track the pet, this would be of limited value in tracking the person.
4) If microchips cause cancer in cats and dogs, it is a very rare occurrence.
The World Small Animal Veterinary Association responded to these claims, which were based on suspicions in lab-rats bred to be susceptible for cancer.
There is no evidence to suggest that companion animals implanted with a microchip are at a higher risk for developing a tumor. The mice used in the studies where an association between a microchip and development of a tumor occurred were genetically predisposed to cancer and do not represent the genetic diversity we see in our dogs and cats. In the United Kingdom where over half of the dog population has a microchip, the British Small Animal Veterinary Association has established a formal system for the reporting of adverse events related to microchips, including tumors. In ten years of collecting data, only 2 tumors were reported to their adverse event registry. When you weigh this extremely rare event against the thousands of pets that are reunited worldwide each year from a microchip, it seems obvious that the benefits from microchipping far outweigh any small risk from a tumor.
5 and 6) Asserting that future governments are conspiring against us is unfalsifiable and off-topic.
The idea that future governments (of which nations?), who presumably aren't in power yet, are conspiring against us in this way is ludicrous. It is also unfalsifiable - no evidence can be produced that would satisfy the conspiracy theorists that make these sorts of claims - so it is out-of-scope of what can be dealt with with scientific evidence.
Aside: If you ignore the blackmarket that would presumably spring up immediately, and the difficulty in policing online transactions, I see no technical reason why many transactions couldn't have an identification requirement, which might include the presentation of an implanted microchip.
