This might be a bit of an over-simplification, but maybe it would help to think of it like this:
Cause = unpleasant situation + unpleasant emotions --> Effect = suffering.
Unpleasant emotions are inseperable from unpleasant situations. The situation is unpleasant because of the unpleasant emotions and conversely the emotions are unpleasant because of the unpleasant situations. So if there is one there will be a mutual-arising of the other. Do you have to suffer from unpleasant situations/emotions? No. Suffering (as has already been pointed out) is something added on to an unpleasant situation, an absolute rejection of an experience as unacceptable. Job interviews aren't inherently unpleasant or anxiety inducing. For those that have anxiety it is usually manageable, in other words, they recognize it as "being anxious," and leave it at that. For some the anxiety is unmanageable, and the stress is suffering. There are various ways for a person to move from suffering anxiety, to managing anxiety:
1. understanding that the situation will pass, that the emotions will pass
2. understanding that neither the situation nor the emotions are "You" or "Yours" just unpleasant "happenings"
3. understanding that the situation/emotions are, by nature of their impermanence and insubstantiality, unsatisfying & stressful.
Unpleasant situations exist, they can't be avoided only managed in a skillful (with equanimity) way. Unpleasant emotions are a result of "ignorance" (or nescience, literally "not knowing.") Suffering is the effect. In this makeshift equation the only variable is nescience. If nescience can be turned to wisdom then suffering can be taken up by its root, and pleasant, unpleasant, neither-pleasant-nor-unpleasant judgements of experience loose their footing.
How is ignorance transformed into wisdom?
1. A calm mind is less reactive (in the sense of less feedback and the resultant backlash of emotions).
2. A concentrated mind is able to see "things as they are" instead of being tinted by desire, aversion, indifference.
3. Seeing "things as they are" produces "insight" or experience of "things as they are," which equates with wisdom.
How does one gain a calm mind?
1. Virtue/Morality = restraint from causing harm in action, speech, thought, intention, livelihood = a mind unburdened from guilt, anger, greed, etc.
2. Samatha-bhavana (meditation) = Cultivation of calm/tranquility through concentration. This temporarily unburdens the mind and gives rise to joy, clarity, and energy.
How does one gain wisdom?
1. (Conceptual) Understanding of "the way things are" aka dhamma.
*Note: This is where one has to initially have "faith" in the Buddha Dhamma, or the Buddha's insight into "the way things are," by taking the time to understand what he is talking about. But have no fear Skeptic, you verify this by:
2. Vipassana-bhavana (meditation) = using the calm concentrated mind to observe what is happening in light of what the Buddha has described, essentially insight into the anicca (impermanent), dukkha (suffering/no lasting satisfaction if nothing lasts), anatta (impermanent self) nature of "things as they are."
I don't think there is anything non-secular about any of these statements. There is a bit of "faith" involved, but no more than accepting that the world is round, or that gravity caused an apple to fall to the earth. Like science the "Dhamma Theory" has been tested and proven by monks and lay persons alike for 2500 years, but unlike science the evidence (nibbana) is not easily demonstrable, so you have to perform the experiments and verify their outcomes on your own using the notes of all those that have done so before you. Fortunately there are signposts and benefits along the way.
Two last pieces of advice:
1. Don't let your expectations get in the way of what is actually happening.
2. Don't get hung up on labels and notions of being "scientific" and "secular" or "mystical" and "spiritual." "Buddhism," as such, simply is what it is. The more you are custom-tailoring it to suit your preferences, the less likely you are to make progress. Be skillful not picky, or you will waste a lot of time making the Dhamma into a personal justification.