Why should different animals have different haemoglobin types

Some animals contain haemoglobin molecules which are structured in way which allows them to have a high affinity for oxygen whilst some are the complete reverse. The reason for this is all to do with the environment in which that organism lives.For example, if an animal lives in a high altitude environment where there is little oxygen available, it would be an advantage to have a haemoglobin type which has a high affinity with oxygen so it can absorb as much as possible from the little there is available.On the opposite end of the spectrum, an animal with a high metabolic rate such as a rodent requires a lot of oxygen to use in cellular respiration. This provides it with  enough energy to carry out its daily routine. Therefore in this case, a haemoglobin type which has a high affinity for oxygen isn't advantageous. Instead, rodents have more haemoglobin which dissociate with oxygen more regularly, releasing it into tissues. Provided, there's enough oxygen in the organisms environment, its far better off having a haemoglobin which releases oxygen more easily than one which takes it up easily.