OK, I had a good laugh. What we are seeing are the "width" features of the error bars. That is, in the unflipped version, we are seeing the horizontal lines drawn at the extremes of the error bar whiskers. The span of the error bars is so small that they are not visible. If I restrict the y axis to a much smaller range, the error bars become visible, sort of.
library(ggplot2)
DF <- structure(list(term = structure(c(10L, 3L, 7L, 11L, 6L, 8L, 9L,
4L, 5L, 2L, 1L),
.Label = c("Wheat and Wheat Products", "Soybeans",
"Eggs", "Poultry", "Rice", "Milk - inc. cheese",
"Fish", "Nuts inc. Peanut Butter","Pork",
"Beef", "Lamb & Goat"), class = "factor"),
estimate = c(30.8578395021078,0.918839779635313, 1.59650962057033,
35.0172960831113, 1.42440472068569,1.77017723354569,
3.55081812529241, 1.07411907826274, 1.27980560328984,
0.399834766499971, 0.190682246067038),
std.error = c(0.00416447057937936,0.00588945077346207, 0.00588945077346208,
0.00590085339938138,0.00588945077346205, 0.00588945077346205,
0.00598522048023851,0.00588945077346199, 0.00588945077346205,
0.00618210531318005,0.00588945077346204),
statistic = c(7409.78688981556, -5083.49604641879,-4968.43101455051,
704.89068266627, -4997.65358665524, -4938.94310138927,
-4562.40859747363, -5057.13037929636, -5022.20581112538,
-4926.80133912833,-5207.13364210929),
p.value = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0),
conf.low = c(30.8496701660344, 0.90728659376472, 1.58495643469974,
35.0057205289993, 1.4128515348151, 1.7586240476751,
3.53907707042253,1.06256589239214, 1.26825241741925,
0.387707487658183, 0.179129060196445),
conf.high = c(30.8660088381812, 0.930392965505906, 1.60806280644093,
35.0288716372233, 1.43595790655629, 1.78173041941628,
3.56255918016229,1.08567226413333, 1.29135878916043,
0.41196204534176, 0.20223543193763)),
class = c("tbl_df", "tbl", "data.frame"), row.names = c(NA,-11L))
ggplot(DF[c(5:11),], aes(term, estimate)) +
geom_point() +
geom_errorbar(aes(ymin = conf.low, ymax = conf.high)) +
coord_flip(expand = TRUE) +
labs(title = "Emissions to Consumption Ratio for \nEach Food Category",
subtitle = "Kilograms of CO2 per Kilogram Consumed") +
ylab("Kilograms of CO2 Emissions of per Kilogram Consumed") +
xlab("Food Category") +
theme_classic() + ylim(0,2)
#> Warning: Removed 1 rows containing missing values (geom_point).

Created on 2020-04-30 by the reprex package (v0.3.0)