Perfect form marks an event that had an important effect on a later situation.
The choice between perfect and simple form is determined by the intention of the speaker to express the relationship between events. For longer passages, the choice of which form to use for each event may vary significantly among writers, according to how each perceives or imagines the relationship among events or wishes to explain them to the reader.
Maybe it has to do with the overall context, so I brought the whole sentences that come before it.
Yes, and it's a good thing you did!
In the excerpt, the fact of Freud being a dog lover late in life has primary importance because it led to a discovery that the dog helps his patients.
The events that caused Freud to be a dog lover have secondary importance. They are mentioned only because they led to an important discovery.
In your reading, the occurrence in the same sentence of the two events [the dog] is given to [Freud] and Freud becomes a dog lover, with only one in perfect form, suggests to you that the writer chose the perfect form to express the relationship between these two events. Because this reading conflicts with the logical and obvious conclusion, the sentence appears incorrect.
However, the writer unfortunately is relying on you to apply your natural understanding of the events to realize that the use of the perfect form in the first clause of the sentence is intended to emphasize the relationship between the sequence of events in this sentence and the sequence of events earlier in the passage.
That is, the writer is expressing that first Freud received the gift and began to love dogs. Then, because of this earlier sequence of events, Freud later observed that the dog helped his patients.
The writer could have chosen perfect form for both clauses, in order to clarify that both events are from an earlier sequence. Some would argue that this choice is better. Indeed, if an editor suggested such a change to me, I would accept it. We cannot know whether the writer considered this possibility.
However, we might guess that the writer simply preferred fewer words and simpler forms to maintain a light feel and natural flow of the text.
The writer may expect that upon finishing the first clause, the reader has already understood that the reason for the perfect form is to express the relation of the events in that clause to the events earlier in the passage. When the reader examines the second clause, he will no longer be considering the reason for the choice to use the perfect form in the previous clause.
The writer seems to prefer a style in which overall comprehension follows from a natural understanding the events, rather than from the choice of each verb form.
In more technical writing, because the relationships among events are not natural to understand from experience, such a choice would be more questionable.