Why would someone not trust an eiruv constructed under respectable rabbis’ supervision? Answer:
The main reason that some people do not carry on Shabbat in an area with an eiruv is actually not a lack of trust in a given rabbi’s expertise, as it is more commonly on fundamental grounds. Rather, they (including some rabbis who are responsible for eiruvin) are not convinced that an eiruv can be effective in the place in question. While all agree to the efficacy of eiruvin, some trust them only for small areas, not city or neighborhood eiruvin. Why?
What most people call an eiruv (a slight misnomer) is a collection of various structures, including walls and sets of strings connecting poles (tzurot hapetach). When an area is sufficiently encompassed with structures, it is a reshut hayachid (private domain, where one may carry, if certain other requirements are met). With all the possible places things that can go wrong in a big eiruv, including a need to rely on certain leniencies and the chance of changes (e.g., fallen or disqualifiedtzurot hapetach) since the last check, there is concern that something will. An eiruv is only as strong as its weakest link.
More fundamentally, the gemara (Eiruvin 6a-b) says that tzurot hapetach do not work in a reshut harabim (public domain, in which carrying more than four amot is forbidden by Torah law). Only in akarmelit (an area with reshut harabim-like status based on Rabbinic law) do tzurot hapesach make an area into a reshut hayachid, in which one may carry. Only actual physical impediments, such as walls and doors/gates can turn a reshut harabim into a reshut hayachid in which one may carry, and these are rarely feasible in municipal settings. Thus, in order to use our standard eiruvin, we need to assume that the areas in question are not reshuyot harabim. Are they?
The only Talmudicly explicit requirements of a reshut harabim are that it is sixteen amot wide (Shabbat 99a), it is not roofed over (ibid. 98a), and perhaps that is frequented by people (Eiruvin 6b). Such places abound (see Rambam, Shabbat 14:1).
How, then, can the great majority of Shabbat-observant Jews use an eiruv that relies on tzurot hapetach? First, rest assured that usage of such eiruvin is indeed the Ashkenazi minhag, supported by leadingposkim for hundreds of years (see Magen Avraham 345:5) and to this day (see Igrot Moshe, OC I:139). The main source of leniency, which the Shulchan Aruch (Orach Chayim 345:7) cites, albeit as a secondary opinion, is that a reshut harabim requires the presence of 600,000 people. The Magen Avraham (ad loc. 5) says that this is the more accepted opinion. The Beur Halacha (ad loc.), while citing manyRishonim who accept it, cites even more Rishonim who are stringent. He also questions the Shulchan Aruch’s contention that the 600,000 must be on an individual street in the course of a normal day. Another "disqualification" of reshuyot harabim is when they are not mefulash(i.e., if streets are lined by buildings on their sides and their openings end or they curve before making it through the city (see Shulchan Aruch, ibid. and Magen Avraham ad loc. 10).
There are other theses to explain our lenient practice (see Aruch Hashulchan, OC 345:20; Chazon Ish 107:5). Perhaps the strongest, found in the Avnei Nezer (OC 273), is that the idea that tzurot hapetachare ineffective in a reshut harabim is just a Rabbinic stringency. After erecting the classic eiruv, then, the worst-case-scenario is only a Rabbinic prohibition, making it is easier to rely on the lenient opinions that a reshut harabim requires 600,000 people.
While we have confirmed the validity of the practice of most of us to rely on eiruvin, we have seen that there are often also strong reasons to refrain from usage, even if an illustrious rabbi vouches for the eiruv. Although we would warn people of the dangers of being machmir on this matter (e.g., due to communal and family dynamics), one should not misinterpret the intention of those who do so.