I've commented on the issue of the 'Ottoman decline thesis' before, so I would recommend that post for a bit of historiographical background.

I think the main issue that gets in the way of laymen understanding what historians are doing when they criticize the use of the term 'decline' is that the term itself can be understood in a myriad of different ways. The first and most obvious question that arises is, "what specifically is in decline?" Historians prior to the revisionism of the late 20th century tended to understand decline holistically, and applied the label to the empire in its every capacity. It wasn't just that the empire was becoming militarily weaker, but that it was also declining economically, administratively, intellectually, etc. Although this decline was influenced by outside causes, it was said to be fundamentally internal. The old view took 'progress' to be the norm, and assumed that if the Ottoman Empire wasn't following along the same trajectory as that of the most advanced countries of western Europe, then something must have been wrong with it internally. Hence 'decline,' and the metaphor of the 'sick man of Europe.' Thus you should recognize that the concept of decline actually applies to far more than just the geopolitical strength of the empire.

In my experience, laymen talking about decline tend to think of it entirely in terms of power-politics. As your post suggests, if you simply look at the capacity of the Ottoman Empire to inflict military defeats on its rivals in the sixteenth century and the late nineteenth century, the empire appears to have declined. It is no doubt true that the empire was relatively less powerful militarily compared to its neighbors in 1900 than it had been in 1600. The problem with jumping from this to saying that the empire was in decline is that it ignores historical nuance. 300 years passed from 1600 to 1900, and it doesn't make sense to label such a massive span of history with a single imprecise term, especially such a heavily loaded one (see my linked post). Thinking in terms of decline encourages a teleological approach to history, namely the belief that history has some kind of goal toward which it is traveling. In this case, the telos (goal) is the dissolution of the empire. In other words, if we say that the empire was in decline, that means attributing a process to the empire's history. But historians find that the Ottomans engaged in plenty of self-strengthening reforms and achieved notable successes at various points during this period of 'decline.' Ultimately the Ottoman Empire did become relatively weaker geopolitically, but this was not due to a single, long-term process spanning hundreds of years. It was the result of many interlocking complex phenomena.

Now that's just one broad, theoretical reason for challenging the idea of decline, and is far from being the only one that historians have used. Another one I would emphasize when addressing a lay audience is the danger of divorcing events from their historical context. That is, it's easy to take some indicator of military strength in one era and to use it as an analogy for the vitality of the whole empire, while contrasting it with another negative analogy from a later period. So, for instance, I've seen many people on the internet say something like this: "The Ottomans besieged Vienna in 1683, but by the twentieth century they were beaten by a coalition of small Balkan states!" The problem with taking this at face value, aside from the above-mentioned issue of ignoring all the history in between, is that it fails to ask why these particular events occurred the way they did. It assumes that both events can be looked at without any nuance, and can be made to stand for the state of the empire as a whole. Its explanation for why the Ottomans lost to a Balkan coalition is simply that "they were weak" or "they were in decline" instead of seeking any meaningful, historically-grounded explanation.

The most in-depth examination of the performance of the Ottoman army in the First Balkan War (1912-3), is that of Edward J. Erickson in his book Defeat in Detail: The Ottoman Army in the Balkans, 1912-1913 (2003). As is clear from the title, he argues that the Ottomans were "defeated in detail," meaning that the Balkan states were able to concentrate their forces in such a way as to engage only a portion of Ottoman strength at any given time. "In short summary, the Ottoman Empire split its field armies into groups and thereby created the conditions necessary for its enemies to achieve numerical superiority on the battlefield" (xvi). This occurred primarily due to the Ottoman military's recent organizational and doctrinal reorganization, carried out alliance with Germany. The Ottomans had adopted a new strategic doctrine with emphasis on offensive maneuvers and envelopment operations. This prevented them from capitalizing on their natural defensive advantages. Also, this military reorganization was only partially complete when the war began, and their troops hadn't had the opportunity to drill for their new maneuvers. The empire was also forced to disperse their army even further due to the danger posed by the Greek navy. The Ottomans had to pull troops off of their offensives early in the war in order to guard against possible coastal attacks, which made a critical difference. Erickson goes on to argue that the Ottoman military was highly adaptive, and was able to quickly carry out the necessary reforms in the aftermath of their defeat. This directly contributed to their unexpectedly stellar performance during World War I.

So it's easy to see that taking the Ottoman defeat in the First Balkan War as an analogy for their 'decline' would be a silly thing to do. Their defeat depended on a lot of contingent circumstances. It wasn't the result of "Ottoman weakness" in some vague sense, but of the specific choices made by the actors involved. If the Ottomans had adopted a defensive doctrine, or had more time to complete their military reorganization before the start of the war, the outcome could have been entirely different. Vague, all-encompassing concepts like 'decline' encourage us to ignore this kind of historical nuance, and to see things in simplistic terms.