The fundamental distinction between 은/는 and 이/가 is that
은/는 tends to state something the speaker knows well, feels strongly about, or otherwise invested some thoughts in. For example, when you introduce yourself, you'd start with 나는 (나는 XX 대학교 다니는 영수야); to say you're happy, 나는 행복하다, since you're saying it because you felt that way in your heart.
이/가 is more about facts and necessity. The speaker says it, often about an external thing rather than what they have been thinking, because the circumstance or context demands it. For example, if you just saw a car speeding by, you might say 차가 너무 빨리 달린다, since you're responding to an unexpected external situation which is a speeding car.
지안은 철수를 좋아한다 is thus stating what the speaker knows or thinks (i.e. he/she saw their behavior and history, and drew this conclusion). Whether it is contrasting or not is largely determined by the context. If there was a mention of another person liking someone, it would be taken as contrasting 지안 to that person; otherwise, it would be an independent sentence.
When asked 누가 컵을 꺴어? (Who broke the cup?), the person answers 제가 깼어요 (I broke it) with 이/가, because he/she is just supplying a fact in response to an external need (the question), not what he/she was thinking about on their own.
은/는 often contrasts things, and this might be a natural consequence of its intrinsic function of expressing subjective thought. For example, if you have two kids A and B and say A is very smart, the implication may be that B is less so, making a contrast between them whether you intended or not.
이/가 has little of this effect, because it's about accidental facts, like "A fire broke out in the downtown last night" (어젯밤에 시내에서 화재가 발생했다), for example.
So 은/는 is the natural way to express one's own thoughts. Most textbooks, Wikipedia articles, and anything explaining something will use it. On the other hand, referring to a specific real life occurrence or anecdotal facts will use 이/가.
Another example on how 은/는 is from what one thinks/knows/feels whereas 이/가 is specific to circumstantial/specific facts.
- 하늘은 푸르다 (The sky is blue). => states what one believes in general.
- 하늘이 노랗다 (The sky is yellow (right now)). => states what one sees at the specific moment.
(it's a figurative way of saying one has acute dizziness/nausea that makes one see things yellow, not a literal statement).
- 내가 부산에 도착했을 때, 거리에는 어둠이 깃들고 있었다 (When I arrived in Busan, darkness was descending on the streets).
You say 내가 because arriving at the place is just supplying a circumstantial fact. It is not something you've been thinking or feeling. 이 in 어둠이 also describes an external occurrence, not your own thought.
(는 in 거리에는 is a different kind of 은/는 usage, not marking a subject but attaching to the particle 에. This adds emphasis or contrast in an adverbial phrase.)